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

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Car X is 40 miles west of Car Y. Both cars are traveling  [#permalink]

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New post Updated on: 01 Oct 2018, 20:45
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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?

Answer:
30 miles per hour



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

Originally posted by kiranck007 on 12 Jun 2013, 09:24.
Last edited by bb on 01 Oct 2018, 20:45, edited 2 times in total.
Renamed the topic, edited the question and the tags.
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Car X is 40 miles west of Car Y. Both cars are traveling  [#permalink]

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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:
30 miles per hour


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  [#permalink]

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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  [#permalink]

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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  [#permalink]

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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  [#permalink]

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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  [#permalink]

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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  [#permalink]

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New post 25 Jan 2014, 03:53
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  [#permalink]

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New post 30 Jul 2014, 20:28
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[size=85]Answer given in the book is (though below answer is copied from beatthegmat.com):


[Obscure] 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[/size
]

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  [#permalink]

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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,
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Re: Car X is 40 miles west of Car Y. Both cars are traveling  [#permalink]

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New post 30 Mar 2018, 11:27
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 &nbs [#permalink] 30 Mar 2018, 11:27
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