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Car A is 20 miles behind car B, which is traveling in the same directi  [#permalink]

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Question Stats: 77% (01:32) correct 23% (02:01) wrong based on 1891 sessions

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Car A is 20 miles behind car B, which is traveling in the same direction along the same route as Car A.Car A is traveling at a constant speed of 58 miles per hour and Car Bis traveling at a constant speed of 50miles per hour.How many hours will it take for Car A to overtake and drive 8 miles ahead of Car B?

A. 1.5
B. 2.0
C. 2.5
D. 3.0
E. 3.5

I tried two formulas to calculate catch up time
1) catch up time when both r moving in same direction=distance between the two/Speed of Car A- Speed of Car B
=> 20/58-50 = 5/2=2.5
to drive 8 miles ahead of Car B by Car A
RT=D
58T=8
T=8/58

Total time= 2.5+8/58 = 2.63 ~=3.0
2) As Car A is 20 miles behind it must have started late than Car B have
so time taken by Car B will be t+x nd
time taken by Car A will be t

As both are moving in the same direction ,both will travel the same distance till catch up time --d

using this information i created two equations and try to solve but
i am not getting correct answer

Originally posted by GMATD11 on 19 Feb 2011, 06:51.
Last edited by Bunuel on 15 Mar 2019, 02:54, edited 1 time in total.
Renamed the topic and edited the question.
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Re: Car A is 20 miles behind car B, which is traveling in the same directi  [#permalink]

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GMATD11 wrote:
Car A is 20 miles behind car B, which is traveling in the same direction along the same route as Car A.Car A is traveling at a constant speed of 58 miles per hour and Car Bis traveling at a constant speed of 50miles per hour. How many hours will it take for Car A to overtake and drive 8 miles ahead of Car B?

a)1.5
b)2.0
c)2.5
d)3.0
e)3.5

I tried two formulas to calculate catch up time
1) catch up time when both r moving in same direction=distance between the two/Speed of Car A- Speed of Car B
=> 20/58-50 = 5/2=2.5
to drive 8 miles ahead of Car B by Car A
RT=D
58T=8
T=8/58

Total time= 2.5+8/58 = 2.63 ~=3.0

2) As Car A is 20 miles behind it must have started late than Car B have
so time taken by Car B will be t+x nd
time taken by Car A will be t

As both are moving in the same direction ,both will travel the same distance till catch up time --d

using this information i created two equations and try to solve but
i am not getting correct answer

Relative speed of car A is 58-50=8 miles per hour, to catch up 20 miles and drive 8 miles ahead so to drive 28 miles it'll need 28/8=3.5 hours.

P.S. The way you are doing it should be 20/8+8/8=2.5+1=3.5 hours.
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Re: Car A is 20 miles behind car B, which is traveling in the same directi  [#permalink]

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Using relative speed concept-
-----------------------------
Relative speed = the distance will shrink between the two cars effectively @ 8 miles per hour

Distance to be covered by A = Difference + Lead = 20 + 8 = 28 miles

Time = Distance / Relative Speed = 28 / 8 = 7/2 = 3.5 hrs.

using time distance concept -
----------------------------
Let t hrs be the time to overtake

Distance traveled by A = 58t miles = 20 + Distance traveled by B = (20 + 50t)

=> 58t = 50t + 20

t = 2.5 hrs

Let k hrs be the time to cover extra 8 miles by A

Distance traveled by A = 58k miles = 8 + Distance traveled by B in k hrs = (8 + 50k) miles

=>8 + 50k = 58k
k = 1.0 hrs

Total time = t + k = 2.5 + 1.0 = 3.5 hrs
##### General Discussion
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Re: Car A is 20 miles behind car B, which is traveling in the same directi  [#permalink]

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Question says that B gets a head start of 20 miles from A.

Say, B traveled x miles when A was already 8 miles ahead of B.

Thus,
Total distance traveled by B = x miles @ speed 50m/h
Total distance traveled by A = 20+x+8 miles @ speed 58m/h ("A" covered the 20m lag; covered the distance x that B covered and got a lead of 8 miles)

It is given that they both traveled these distances in the same time/duration;
Time spent by B = Time spent by A

Time = Distance/Speed

x/50 = (20+x+8)/58
58x = 1000+50x+400
8x = 1400
x = 175 miles

We know the value of x.

We need to find out the time taken by A to travel the distance = 20+x+8 = 20+175+8 = 203miles

A traveled the distance of 203 @ 58m/h in 203/58 h = 3.5h.

Ans: "E"
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Re: Car A is 20 miles behind car B, which is traveling in the same directi  [#permalink]

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5
3
Just making some formulas :

1. If Objects move in samedirection : The relative speed can be Added / Substracted .
ie. If Car A is moving at X km/hr and Car B is moving at Y km/hr . X > Y
imagine car B to be stopped at car A moving at X-Y km/hr

2. If Objects moving in oppdirection (towards OR away from each other)
if If Car A is moving at X km/hr from Left to right And Car B @ Y km/hr from R2L
imagine car B stationary and A moving toward it at X+Y kms/hr

-Eski
Intern  Joined: 20 Mar 2013
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Re: Car A is 20 miles behind car B, which is traveling in the same directi  [#permalink]

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car a 58mph...car b 50mph..so in 1hour..car goes 8mile ahead..to cover 20mile car a will take 2.5hr..hence an additional 1hour to go 8mile ahead..hence 3.5 in total
Intern  Joined: 19 Feb 2013
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Re: Car A is 20 miles behind car B, which is traveling in the same directi  [#permalink]

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Bunuel wrote:
GMATD11 wrote:
Car A is 20 miles behind car B, which is traveling in the same direction along the same route as Car A.Car A is traveling at a constant speed of 58 miles per hour and Car Bis traveling at a constant speed of 50miles per hour. How many hours will it take for Car A to overtake and drive 8 miles ahead of Car B?

a)1.5
b)2.0
c)2.5
d)3.0
e)3.5

I tried two formulas to calculate catch up time
1) catch up time when both r moving in same direction=distance between the two/Speed of Car A- Speed of Car B
=> 20/58-50 = 5/2=2.5
to drive 8 miles ahead of Car B by Car A
RT=D
58T=8
T=8/58

Total time= 2.5+8/58 = 2.63 ~=3.0

2) As Car A is 20 miles behind it must have started late than Car B have
so time taken by Car B will be t+x nd
time taken by Car A will be t

As both are moving in the same direction ,both will travel the same distance till catch up time --d

using this information i created two equations and try to solve but
i am not getting correct answer

Relative speed of car A is 58-50=8 miles per hour, to catch up 20 miles and drive 8 miles ahead so to drive 28 miles it'll need 28/8=3.5 hours.

P.S. The way you are doing it should be 20/8+8/8=2.5+1=3.5 hours.

Car A need to drive 28 mile, so time for A= 28/58
But as car B is moving too 28/58-8/50=3
Can you help me, what i am missing?
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Re: Car A is 20 miles behind car B, which is traveling in the same directi  [#permalink]

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Marchikn wrote:
Car A need to drive 28 mile, so time for A= 28/58
But as car B is moving too 28/58-8/50=3
Can you help me, what i am missing?

Hi Marchikn, you are missing the fact that while a "catches up" B is still driving forward.

Here is my solution: $$speedA = 58, speedB=50$$ this means that every hour A gains $$58-50=8$$ miles on B.
In how many hours will A reach B?
space=time*speed, space = distance between cars, speed is the rate at which A is catching up (difference of the speeds A-B)
$$t=\frac{20}{8}=2.5h$$ A will take 2.5 h to reach B.
But the question asks "when A will be 8 miles ahead", so we need to add to this time the time it will take A to do so.
$$8=t*8$$, $$t=1$$, 1h to get 8 miles ahead + 2.5 h to reach B = $$3.5h$$

Let me know if it's clear.
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Posts: 10664
Location: Pune, India
Re: Car A is 20 miles behind car B, which is traveling in the same directi  [#permalink]

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2
5
Marchikn wrote:
Bunuel wrote:
GMATD11 wrote:
Car A is 20 miles behind car B, which is traveling in the same direction along the same route as Car A.Car A is traveling at a constant speed of 58 miles per hour and Car Bis traveling at a constant speed of 50miles per hour. How many hours will it take for Car A to overtake and drive 8 miles ahead of Car B?

a)1.5
b)2.0
c)2.5
d)3.0
e)3.5

I tried two formulas to calculate catch up time
1) catch up time when both r moving in same direction=distance between the two/Speed of Car A- Speed of Car B
=> 20/58-50 = 5/2=2.5
to drive 8 miles ahead of Car B by Car A
RT=D
58T=8
T=8/58

Total time= 2.5+8/58 = 2.63 ~=3.0

2) As Car A is 20 miles behind it must have started late than Car B have
so time taken by Car B will be t+x nd
time taken by Car A will be t

As both are moving in the same direction ,both will travel the same distance till catch up time --d

using this information i created two equations and try to solve but
i am not getting correct answer

Relative speed of car A is 58-50=8 miles per hour, to catch up 20 miles and drive 8 miles ahead so to drive 28 miles it'll need 28/8=3.5 hours.

P.S. The way you are doing it should be 20/8+8/8=2.5+1=3.5 hours.

Car A need to drive 28 mile, so time for A= 28/58
But as car B is moving too 28/58-8/50=3
Can you help me, what i am missing?

The concept being used here is relative speed. Check out my post:
http://www.veritasprep.com/blog/2012/07 ... elatively/

Time taken by A = 28/(58 - 50) = 3.5 hrs
We subtract 50 because of what you said - B is moving too and B's speed is 50. The concept will be clear once you through the post.
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Re: Car A is 20 miles behind car B, which is traveling in the same directi  [#permalink]

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1
Let t be time car A needs to overtake car B and drive 8 miles ahead. Then:

58t - 20 = 50t + 8

t=28/8=3.5 hours

Hope this helps

Posted from my mobile device
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Re: Car A is 20 miles behind car B, which is traveling in the same directi  [#permalink]

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Hi Karishma,

veritasprep/blog/2012/07/quarter-wit-quarter-wisdom-speeding-relatively/

Could you please share the next week doc which is mentioned there for some tougher relative speed questions?

"Next week, we will look at some tougher relative speed questions"
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Re: Car A is 20 miles behind car B, which is traveling in the same directi  [#permalink]

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Nishant1234567 wrote:
Hi Karishma,

veritasprep/blog/2012/07/quarter-wit-quarter-wisdom-speeding-relatively/

Could you please share the next week doc which is mentioned there for some tougher relative speed questions?

"Next week, we will look at some tougher relative speed questions"

Here are two posts discussing relative speed questions:
http://www.veritasprep.com/blog/2012/08 ... -speeding/
http://www.veritasprep.com/blog/2012/08 ... -concepts/

P.S. - In case you are looking for posts on particular topics, just use the search feature e.g. type "relative speed quarter wit" in the Search field of our blog.
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Re: Car A is 20 miles behind car B, which is traveling in the same directi  [#permalink]

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Bunuel wrote:
GMATD11 wrote:
Car A is 20 miles behind car B, which is traveling in the same direction along the same route as Car A.Car A is traveling at a constant speed of 58 miles per hour and Car Bis traveling at a constant speed of 50miles per hour. How many hours will it take for Car A to overtake and drive 8 miles ahead of Car B?

a)1.5
b)2.0
c)2.5
d)3.0
e)3.5

I tried two formulas to calculate catch up time
1) catch up time when both r moving in same direction=distance between the two/Speed of Car A- Speed of Car B
=> 20/58-50 = 5/2=2.5
to drive 8 miles ahead of Car B by Car A
RT=D
58T=8
T=8/58

Total time= 2.5+8/58 = 2.63 ~=3.0

2) As Car A is 20 miles behind it must have started late than Car B have
so time taken by Car B will be t+x nd
time taken by Car A will be t

As both are moving in the same direction ,both will travel the same distance till catch up time --d

using this information i created two equations and try to solve but
i am not getting correct answer

Relative speed of car A is 58-50=8 miles per hour, to catch up 20 miles and drive 8 miles ahead so to drive 28 miles it'll need 28/8=3.5 hours.

P.S. The way you are doing it should be 20/8+8/8=2.5+1=3.5 hours.

Hi Bunuel,

Can you please guide me to the location of additional relative rate problems?

Thanks!
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Posts: 10664
Location: Pune, India
Re: Car A is 20 miles behind car B, which is traveling in the same directi  [#permalink]

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I am sure Bunuel will give you a dozen links for practice questions but meanwhile, here are some of my posts with relative speed practice questions:

http://www.veritasprep.com/blog/2012/07 ... elatively/
http://www.veritasprep.com/blog/2012/08 ... -speeding/
http://www.veritasprep.com/blog/2012/08 ... -concepts/
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Re: Car A is 20 miles behind car B, which is traveling in the same directi  [#permalink]

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1
1
I find it easier to understand by looking at the distances:

lets say distance of car A is (Rate x Time) ---> 58xTime
car B is ---> 50xTime

So at some Time car A with its 58 miles per hour rate: will manage to cover 20 miles to break even + 8 miles to get ahead

Distance of A = Distance of B +20 +8
58xTime = 50xTime + 28

8Time = 28
Time = 3.5
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Re: Car A is 20 miles behind car B, which is traveling in the same directi  [#permalink]

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GMATD11 wrote:
Car A is 20 miles behind car B, which is traveling in the same direction along the same route as Car A.Car A is traveling at a constant speed of 58 miles per hour and Car Bis traveling at a constant speed of 50miles per hour.How many hours will it take for Car A to overtake and drive 8 miles ahead of Car B?

A. 1.5
B. 2.0
C. 2.5
D. 3.0
E. 3.5

We can classify this problem as a “catch up and pass” rate question. This means that one car is catching up to the other car and passing it by some distance.

Since there is a change in rate as well as a change in distance between the two cars, we can use the formula:

time = (change in distance)/(change in rate)

We are given that car A is 20 miles behind car B and we need to determine the time when car A is 8 miles ahead of car B. Thus, we can say that the change in distance is 20 + 8 = 28 miles.

We are also given that car A travels at a constant speed of 58 mph and car B travels a constant speed of 50 miles per hour. Thus, we can say that the change in rate is 58 – 50 = 8 mph.

We can plug this information into our equation:

time = (change in distance)/(change in rate)

time = 28/8 = 7/2 = 3.5 hours

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Re: Car A is 20 miles behind car B, which is traveling in the same directi  [#permalink]

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GMATD11 wrote:
Car A is 20 miles behind car B, which is traveling in the same direction along the same route as Car A.Car A is traveling at a constant speed of 58 miles per hour and Car Bis traveling at a constant speed of 50miles per hour.How many hours will it take for Car A to overtake and drive 8 miles ahead of Car B?

A. 1.5
B. 2.0
C. 2.5
D. 3.0
E. 3.5

I tried two formulas to calculate catch up time
1) catch up time when both r moving in same direction=distance between the two/Speed of Car A- Speed of Car B
=> 20/58-50 = 5/2=2.5
to drive 8 miles ahead of Car B by Car A
RT=D
58T=8
T=8/58

Total time= 2.5+8/58 = 2.63 ~=3.0
2) As Car A is 20 miles behind it must have started late than Car B have
so time taken by Car B will be t+x nd
time taken by Car A will be t

As both are moving in the same direction ,both will travel the same distance till catch up time --d

using this information i created two equations and try to solve but
i am not getting correct answer

Hope this illustration helps
Attachments

File comment: Does this help? c1c2.PNG [ 8.64 KiB | Viewed 26097 times ]

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Re: Car A is 20 miles behind car B, which is traveling in the same directi  [#permalink]

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For each catch up or meeting questions; I've found that relative speed concept is very useful!

1. When catching up, the relative speed is the difference between rate A vs rate B = which is 58 mph - 50 mph = 8 mph.

2. First, we want to to know when the A catch up the B :
- Rate : 8 mph
- Distance : 20 miles (since 20 miles is the difference)
- So, we can calculate Time = $$\frac{Distance}{Rate}$$ = $$\frac{20}{8}$$ = 2,5 hrs.

3. Second, since we must calculate when A is 8 miles ahead, so we must calculate how much time A will set this difference.
- Rate : 8 mph
- Distance : 8 miles (we want to set 8 miles difference)
- Time = $$\frac{Distance}{Rate}$$ =$$\frac{8}{8}$$= 1 hour

4. The sum of number (2) and (3) is the answer = 3,5 hrs. Hence E.
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Re: Car A is 20 miles behind car B, which is traveling in the same directi  [#permalink]

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[quote="GMATD11"]Car A is 20 miles behind car B, which is traveling in the same direction along the same route as Car A.Car A is traveling at a constant speed of 58 miles per hour and Car Bis traveling at a constant speed of 50miles per hour.How many hours will it take for Car A to overtake and drive 8 miles ahead of Car B?

A. 1.5
B. 2.0
C. 2.5
D. 3.0
E. 3.5

Using simple formula ---
Time(difference) = distance(difference)/speed(difference)
t= 20/58-50=> 2.5hrs

2.5hrs —> 20 miles
x hrs —> 8 miles => solving for x => 2.5*8/20 => 1hr

total time= 2.5+1 => 3.5 hrs (option C)
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Re: Car A is 20 miles behind car B, which is traveling in the same directi  [#permalink]

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_________________ Re: Car A is 20 miles behind car B, which is traveling in the same directi   [#permalink] 10 Oct 2019, 22:54

# Car A is 20 miles behind car B, which is traveling in the same directi  