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Car X is 40 miles west of Car Y. Both cars are traveling east, and Car

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kiranck007
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Car X is 40 miles west of Car Y. Both cars are traveling east, and Car [#permalink] New post   Updated on: 01 Jul 2019, 01:45
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Car X is 40 miles west of Car Y. Both cars are traveling east, and Car X is going 50% faster than Car Y. If both cars travel at a constant rate and it takes Car X 2 hours and 40 minutes to catch up to Car Y, how fast is Car Y going?

A. 20 miles per hour
B. 25 miles per hour
C. 30 miles per hour
D. 35 miles per hour
E. 40 miles per hour

Show Spoiler
Let speed of Y = V ,
speed of X = 1.5 V,
relative speed of X wrt Y (catch up speed of X) = 0.5V.
Now catch up speed = (distance between X and Y)/time.

0.5 V = 40 miles / (8/3 hour),
so V = 30 miles/hr.

However, what I don't understand is that the distance traveled by Car Y while Car X is catching up is not factored into the problem. Could someone clarify if my concern is valid, if not then reason.

Thanks,
Kiran
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C

Originally posted by kiranck007 on 12 Jun 2013, 09:24.
Last edited by Bunuel on 01 Jul 2019, 01:45, edited 3 times in total.
Renamed the topic, edited the question and the tags.
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Bunuel
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Re: Car X is 40 miles west of Car Y. Both cars are traveling east, and Car [#permalink] New post   12 Jun 2013, 09:41
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kiranck007 wrote:
Car X is 40 miles west of Car Y. Both cars are traveling east, and Car X is going 50% faster than Car Y. If both cars travel at a constant rate and it takes Car X 2 hours and 40 minutes to catch up to Car Y, how fast is Car Y going?

Answer:
Show Spoiler
30 miles per hour


Show Spoiler
Let speed of Y = V ,
speed of X = 1.5 V,
relative speed of X wrt Y (catch up speed of X) = 0.5V.
Now catch up speed = (distance between X and Y)/time.

0.5 V = 40 miles / (8/3 hour),
so V = 30 miles/hr.

However, what I don't understand is that the distance traveled by Car Y while Car X is catching up is not factored into the problem. Could someone clarify if my concern is valid, if not then reason.

Thanks,
Kiran


Say the rate of Car Y is y miles per hour and the rate of Car X is 1.5y miles per hour..

Since they are traveling in the same direction their relative speed is 1.5y-y=0.5y=y/2 miles per hour.

Time*Rate=Distance --> (8/3)*(y/2)=40 --> y=30 miles per hour.
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Re: Car X is 40 miles west of Car Y. Both cars are traveling east, and Car [#permalink] New post   15 Aug 2013, 11:07
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Car X is 40 miles west of Car Y. Both cars are traveling east, and Car X is going 50% faster than Car Y. If both cars travel at a constant rate and it takes Car X 2 hours and 40 minutes to catch up to Car Y, how fast is Car Y going?

Basically, this problem is no different than if Y were stationary and it took x 2.66 hours to catch up to it. However, we need to consider that they are moving and that car X is traveling at a speed 1.5times y.

Speed of y = y
Speed of x = 1.5y
distance = 40

The relative speed of x compared to y is 1.5y - y = 0.5y

time = distance/speed
8/3 = 40/0.5y
4y=120
y=30

We use the relative speed in this formula (as opposed to the speed of x or y) because it's in the context of the time and distance x must cover to reach y. Thus, we use the relative speed of x compared to y. Once we obtain y, we can plug it into the actual speeds of x and y (1.5y and y respectively)

speed of y = 30
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Re: Car X is 40 miles west of Car Y. Both cars are traveling east, and Car [#permalink] New post   29 Mar 2018, 07:44
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kiranck007 wrote:
Car X is 40 miles west of Car Y. Both cars are traveling east, and Car X is going 50% faster than Car Y. If both cars travel at a constant rate and it takes Car X 2 hours and 40 minutes to catch up to Car Y, how fast is Car Y going?


Let's let Car X's original position be the initial starting point.
So, when Car X is at the initial starting point, Car Y has already traveled 40 miles.

My word equation involves the conditions when Car X catches up to Car Y.
At that point, we can say:
Car X's TOTAL distance traveled = Car Y's TOTAL distance traveled

Car Y's total distance
Let V = Car Y's speed (our goal is to find the value of V)
From the time that Car X begins moving, Car Y drives for 2 2/3 hours (2 hours, 40 minutes).
So Car Y's total distance = (time)(speed) = (2 2/3)(V) + 40 miles

Car X's total distance
We know that Car X is going 50% faster than Car Y. If Car Y's rate is V, then Car X's rate must be 1.5V
We also know that Car X travels for 2 2/3 hours.
So Car X's total distance = (time)(speed) = (2 2/3)(1.5V) miles
Simplify: (2 2/3)(1.5V) = (8/3)(3/2) = 4V

We're now ready to write our algebraic equation.
Car X's total distance = Car Y's total distance
4V = (2 2/3)(V) + 40 miles
4/3V = 40
V = 40(3/4)
V = 30

Cheers,
Brent
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Re: Car X is 40 miles west of Car Y. Both cars are traveling east, and Car [#permalink] New post   19 Jan 2014, 08:08
Bunuel wrote:
Time*Rate=Distance --> 8/3*y/2=40 --> y=30 miles per hour.



How did we arrive to 8/3 hours.... as its given 2.40 hours which is 160 mins.... what have I mistaken out here, can someone point it out to me.

Thanks in advance!
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Re: Car X is 40 miles west of Car Y. Both cars are traveling east, and Car [#permalink] New post   19 Jan 2014, 08:28
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patternpandora wrote:
Bunuel wrote:
Time*Rate=Distance --> 8/3*y/2=40 --> y=30 miles per hour.



How did we arrive to 8/3 hours.... as its given 2.40 hours which is 160 mins.... what have I mistaken out here, can someone point it out to me.

Thanks in advance!



You have to convert 160 minutes into hours because it is asked for mph!

\(\frac{160}{60} = \frac{16}{6} = \frac{8}{3}\)

You could also do that in the end:

\((1.5y-1y)\frac{m}{h} x 160min = 40miles\)

\(0.5y\frac{m}{h} = \frac{40miles}{160min}\)

\(y\frac{m}{h} = \frac{80miles}{160min} = \frac{1miles}{2min} = \frac{60miles}{2hours} = 30\frac{miles}{hour}\)
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Re: Car X is 40 miles west of Car Y. Both cars are traveling east, and Car [#permalink] New post   19 Jan 2014, 10:08
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patternpandora wrote:
Bunuel wrote:
Time*Rate=Distance --> 8/3*y/2=40 --> y=30 miles per hour.



How did we arrive to 8/3 hours.... as its given 2.40 hours which is 160 mins.... what have I mistaken out here, can someone point it out to me.

Thanks in advance!


2 hours and 40 minutes = \(2\frac{2}{3}\) hours= \(\frac{8}{3}\) hours.
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Re: Car X is 40 miles west of Car Y. Both cars are traveling east, and Car [#permalink] New post   25 Jan 2014, 03:27
Do you have more such question in relative speed?


Bunuel wrote:
patternpandora wrote:
Bunuel wrote:
Time*Rate=Distance --> 8/3*y/2=40 --> y=30 miles per hour.



How did we arrive to 8/3 hours.... as its given 2.40 hours which is 160 mins.... what have I mistaken out here, can someone point it out to me.

Thanks in advance!


2 hours and 40 minutes = \(2\frac{2}{3}\) hours= \(\frac{8}{3}\) hours.
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Re: Car X is 40 miles west of Car Y. Both cars are traveling east, and Car [#permalink] New post   25 Jan 2014, 03:53
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ROckHIsT wrote:
Do you have more such question in relative speed?



Theory on Distance/Rate Problems: distance-speed-time-word-problems-made-easy-87481.html

All DS Distance/Rate Problems to practice: search.php?search_id=tag&tag_id=44
All PS Distance/Rate Problems to practice: search.php?search_id=tag&tag_id=64
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Re: Car X is 40 miles west of Car Y. Both cars are traveling east, and Car [#permalink] New post   30 Jul 2014, 20:28
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Let speed of Y = V ,
speed of X = 1.5 V,
relative speed of X wrt Y (catch up speed of X) = 0.5V.
Now catch up speed = (distance between X and Y)/time.

0.5 V = 40 miles / (8/3 hour),
so V = 30 miles/hr.

However, what I don't understand is that the distance traveled by Car Y while Car X is catching up is not factored into the problem. Could someone clarify if my concern is valid, if not then reason.

Thanks,
Kiran[/size[/i][/color]]

Refer diagram below

\(160 Mins = \frac{160}{60} Hrs = \frac{8}{3}\)

Time required by X to reach catch point = Time required by Y to reach catch point \(= \frac{8}{3}\)

\(\frac{40+d}{\frac{150s}{100}} = \frac{d}{s}\)

3d = 2d + 80

d = 80

\(s = \frac{80}{\frac{8}{3}}\)

s = 30
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Re: Car X is 40 miles west of Car Y. Both cars are traveling east, and Car [#permalink] New post   30 Mar 2018, 11:27
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kiranck007 wrote:
Car X is 40 miles west of Car Y. Both cars are traveling east, and Car X is going 50% faster than Car Y. If both cars travel at a constant rate and it takes Car X 2 hours and 40 minutes to catch up to Car Y, how fast is Car Y going?


We can let the rate of Car Y = r and the rate of Car X = 1.5r. Recall that 2 hours and 40 minutes = 2 2/3 hours = 8/3 hours.

We can create the equation:

1.5r(8/3) = r(8/3) + 40

12r/3 = 8r/3 + 40

4r/3 = 40

4r = 120

r = 30
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Re: Car X is 40 miles west of Car Y. Both cars are traveling east, and Car [#permalink] New post   23 Dec 2018, 01:18
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kiranck007 wrote:
Car X is 40 miles west of Car Y. Both cars are traveling east, and Car X is going 50% faster than Car Y. If both cars travel at a constant rate and it takes Car X 2 hours and 40 minutes to catch up to Car Y, how fast is Car Y going?

Answer:
Show Spoiler
30 miles per hour



Show Spoiler
Let speed of Y = V ,
speed of X = 1.5 V,
relative speed of X wrt Y (catch up speed of X) = 0.5V.
Now catch up speed = (distance between X and Y)/time.

0.5 V = 40 miles / (8/3 hour),
so V = 30 miles/hr.

However, what I don't understand is that the distance traveled by Car Y while Car X is catching up is not factored into the problem. Could someone clarify if my concern is valid, if not then reason.

Thanks,
Kiran

Speed of Car Y = x => Speed of Car X = 1.5x (miles/h)
Distance = 40 miles
Catch up time = Distance between X&Y/ Different speed between X&Y => 40/(1.5x - x) = 2h40mins = 8/3 hours (40mins = 2/3 hour)
=> x = 30 miles/hr
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Re: Car X is 40 miles west of Car Y. Both cars are traveling east, and Car [#permalink] New post   01 Jul 2019, 02:39
kiranck007 wrote:
Car X is 40 miles west of Car Y. Both cars are traveling east, and Car X is going 50% faster than Car Y. If both cars travel at a constant rate and it takes Car X 2 hours and 40 minutes to catch up to Car Y, how fast is Car Y going?

A. 20 miles per hour
B. 25 miles per hour
C. 30 miles per hour
D. 35 miles per hour
E. 40 miles per hour

Show Spoiler
Let speed of Y = V ,
speed of X = 1.5 V,
relative speed of X wrt Y (catch up speed of X) = 0.5V.
Now catch up speed = (distance between X and Y)/time.

0.5 V = 40 miles / (8/3 hour),
so V = 30 miles/hr.

However, what I don't understand is that the distance traveled by Car Y while Car X is catching up is not factored into the problem. Could someone clarify if my concern is valid, if not then reason.

Thanks,
Kiran


Using ratio approach to solve this problem

It's given that speed of X is 50% more than speed of Y---------> Speed of X =3/2 * Speed of Y

We can take speed of X=3k and Speed of Y=2K (I'm using K because I don't know the actual quantity)

X will cover 40 miles in 2 hours 40 minutes which means that the difference between X and Y of 40 miles is covered by X in 2 hours 40 minutes

Difference of X and Y covered by X (speed)= (40)/(8/3)= (40*3)/8 = 15 miles every hour-----------> Equation 1

Difference of X and Y = 3k-2k = K ---------------> Equation 2

Equating both of them we get

k=15 miles per hour.

Speed of Y= 2K = 2*15 mph= 30 miles per hour
Speed of X= 3*15 mph= 45 miles per hour.
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Re: Car X is 40 miles west of Car Y. Both cars are traveling east, and Car [#permalink] New post   28 Sep 2019, 04:37
speed of y ; a
speed of x ; 1.5a
given time ; 2 hrs 40 mins ; 160 mins ; 160/60 ; 8/3 hrs

from given info we can say
1.5a*8/3 = 40+ 8*a/3
solve for a = 30 mph
IMO C

kiranck007 wrote:
Car X is 40 miles west of Car Y. Both cars are traveling east, and Car X is going 50% faster than Car Y. If both cars travel at a constant rate and it takes Car X 2 hours and 40 minutes to catch up to Car Y, how fast is Car Y going?

A. 20 miles per hour
B. 25 miles per hour
C. 30 miles per hour
D. 35 miles per hour
E. 40 miles per hour

Show Spoiler
Let speed of Y = V ,
speed of X = 1.5 V,
relative speed of X wrt Y (catch up speed of X) = 0.5V.
Now catch up speed = (distance between X and Y)/time.

0.5 V = 40 miles / (8/3 hour),
so V = 30 miles/hr.

However, what I don't understand is that the distance traveled by Car Y while Car X is catching up is not factored into the problem. Could someone clarify if my concern is valid, if not then reason.

Thanks,
Kiran
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Re: Car X is 40 miles west of Car Y. Both cars are traveling east, and Car [#permalink] New post   30 Oct 2019, 09:17
speed of y = s
speed of x= 1.5s
relative speed = .5s
distance = 40 miles
time ; 160 mins ; 160/60 ; 8/3 hrs
40=8/3 * .5s
s= 30 mph
IMO C


kiranck007 wrote:
Car X is 40 miles west of Car Y. Both cars are traveling east, and Car X is going 50% faster than Car Y. If both cars travel at a constant rate and it takes Car X 2 hours and 40 minutes to catch up to Car Y, how fast is Car Y going?

A. 20 miles per hour
B. 25 miles per hour
C. 30 miles per hour
D. 35 miles per hour
E. 40 miles per hour

Show Spoiler
Let speed of Y = V ,
speed of X = 1.5 V,
relative speed of X wrt Y (catch up speed of X) = 0.5V.
Now catch up speed = (distance between X and Y)/time.

0.5 V = 40 miles / (8/3 hour),
so V = 30 miles/hr.

However, what I don't understand is that the distance traveled by Car Y while Car X is catching up is not factored into the problem. Could someone clarify if my concern is valid, if not then reason.

Thanks,
Kiran
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Car X is 40 miles west of Car Y. Both cars are traveling east, and Car [#permalink] New post   25 Feb 2020, 09:22
GMATPrepNow wrote:
kiranck007 wrote:
Car X is 40 miles west of Car Y. Both cars are traveling east, and Car X is going 50% faster than Car Y. If both cars travel at a constant rate and it takes Car X 2 hours and 40 minutes to catch up to Car Y, how fast is Car Y going?


Let's let Car X's original position be the initial starting point.
So, when Car X is at the initial starting point, Car Y has already traveled 40 miles.

My word equation involves the conditions when Car X catches up to Car Y.
At that point, we can say:
Car X's TOTAL distance traveled = Car Y's TOTAL distance traveled

Car Y's total distance
Let V = Car Y's speed (our goal is to find the value of V)
From the time that Car X begins moving, Car Y drives for 2 2/3 hours (2 hours, 40 minutes).
So Car Y's total distance = (time)(speed) = (2 2/3)(V) + 40 miles

Car X's total distance
We know that Car X is going 50% faster than Car Y. If Car Y's rate is V, then Car X's rate must be 1.5V
We also know that Car X travels for 2 2/3 hours.
So Car X's total distance = (time)(speed) = (2 2/3)(1.5V) miles
Simplify: (2 2/3)(1.5V) = (8/3)(3/2) = 4V

We're now ready to write our algebraic equation.
Car X's total distance = Car Y's total distance
4V = (2 2/3)(V) + 40 miles
4/3V = 40
V = 40(3/4)
V = 30

Cheers,
Brent



hi GMATPrepNow Brent :)

what is the reason that you attribute 40 miles to Y Car ? Car X still have to do more than 40 miles :) I ask this question because i see other solutions in this thread, attributing 40 miles to car X as well :?

Or maybe it doesn`t matter :grin:

thanks :)
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Re: Car X is 40 miles west of Car Y. Both cars are traveling east, and Car [#permalink] New post   25 Feb 2020, 10:29
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dave13 wrote:
GMATPrepNow wrote:

hi GMATPrepNow Brent :)

what is the reason that you attribute 40 miles to Y Car ? Car X still have to do more than 40 miles :) I ask this question because i see other solutions in this thread, attributing 40 miles to car X as well :?

Or maybe it doesn`t matter :grin:

thanks :)


All that really matters is that we start with a 40-mile gap between the two cars.

However, since Car X is 40 miles west of Car Y, and since the cars are travelling east, we see that Car Y is originally 40 miles ahead of Car X.
So, when the two cars are at the same position, Car X will have travelled 40 miles further than Car Y.
To account for this (and create an equation) we need to add 40 miles to Car Y's travel distance.

Does that help?

Cheers,
Brent
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Re: Car X is 40 miles west of Car Y. Both cars are traveling east, and Car [#permalink] New post   27 Nov 2023, 23:10
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kiranck007 wrote:
Car X is 40 miles west of Car Y. Both cars are traveling east, and Car X is going 50% faster than Car Y. If both cars travel at a constant rate and it takes Car X 2 hours and 40 minutes to catch up to Car Y, how fast is Car Y going?

A. 20 miles per hour
B. 25 miles per hour
C. 30 miles per hour
D. 35 miles per hour
E. 40 miles per hour

Show Spoiler
Let speed of Y = V ,
speed of X = 1.5 V,
relative speed of X wrt Y (catch up speed of X) = 0.5V.
Now catch up speed = (distance between X and Y)/time.

0.5 V = 40 miles / (8/3 hour),
so V = 30 miles/hr.

However, what I don't understand is that the distance traveled by Car Y while Car X is catching up is not factored into the problem. Could someone clarify if my concern is valid, if not then reason.

Thanks,
Kiran


The questions uses relative speed. Both cars are going in the same direction (East) with X 40 miles behind Y. The ratio of their speeds is 3:2 so the difference between them is the speed of X relative to Y. This speed is what will decide the time X takes to overtake Y
Distance between X and Y = 40 miles
Time taken by X to overtake Y = 2 hr 40 mins = 8/3 hrs
Speed of X relative to Y = 40/(8/3) = 15 mph

3 : 2 Diff on ratio scale = 1 which is actually 15. Hence the multiplier is 15 and their speeds are 45 mph (of X) and 30 mph (of Y).

Answer (C)


Check this video to know how to recognise relative speed questions: https://youtu.be/wrYxeZ2WsEM
Check these videos to learn how to use ratios to do these calculations orally:
https://youtu.be/5ODENGG5dvc
https://youtu.be/7ASEIvxYPCM
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Re: Car X is 40 miles west of Car Y. Both cars are traveling east, and Car [#permalink]
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