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

Question

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 B is 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

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
But answer is different
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

Bunuel · Accepted 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.

Answer: E.

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

gmat1220 · Answer

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

fluke · Answer

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"

eski · Answer

Just making some formulas :

1. If Objects move in  same direction : 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  opp direction (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

mahmudratul · Answer

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

Marchikn · Answer

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?

Zarrolou · Answer

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.

KarishmaB · Answer

The concept being used here is relative speed.

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.

spla626 · Answer

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

KarishmaB · Answer

Here are some of my videos with relative speed practice questions: https://youtu.be/wrYxeZ2WsEM https://youtu.be/EDsHa_CULmg

JeffTargetTestPrep · Answer

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

The answer is E.

kvsahi08 · Answer

If there is an initial difference between the 2 people, driving in the same direction, the time take for them to meet = initial difference in distance \ (speed of a-speed of b). But if want to know when A will overtake B by x miles, we can add that difference in the distance to the initial difference in the formula.

=> (initial difference in distance + miles to overtake)/(speed of a - speed of b)
=> (20+8)/(58-50) 
=> 28/8
=> 3.5hr.

BrentGMATPrepNow · Answer

Here is an illustration of what's happening:
 https://i.imgur.com/DnQ8aHm.png 
As you can see, car B drives from line X to line Y, whereas car A drives from line W to line Z, which means car A drives the same distance that car B drives PLUS an additional 28 miles.

APPROACH #1 : Start with a word equation
The question tells us that Car A's total travel distance is 28 miles greater than Car B's total travel distance.
So we can write:  ( Car A's travel distance ) - ( Car B's travel distance ) = 28 miles

Let t = Car A's travel time, which means t = Car B's travel also. 
 Distance = (rate)(time)

Plug our values into the word equation to get:   58t  -  50t  = 28 
Subtract 50t from both sides:  8t = 28 
Solve:  t = 28/8 = 7/2 = 3.5 
Answer: E

APPROACH #2 : Answer the question in two parts
58 mph - 50 mph =  8  mph. 
So, the original 20 mile gap between the two cars shrinks at a rate of  8  mph. 
Time to reduce the gap to zero = distance/rate = 20/ 8  = 2.5 hours.
Time to increase the gap from 0 to 8 miles = distance/rate = 8/ 8  = 1 hour.
So, the total time for car A go from being 20 miles behind to being 8 miles ahead = 2.5 hours + 1 hour = 3.5 hours 
Answer: E

ArnauG · Answer

To calculate the time it takes for Car A to overtake and drive 8 miles ahead of Car B, we need to determine the relative speed between the two cars.

The relative speed is the difference between the speeds of the two cars. In this case, Car A is traveling at 58 miles per hour and Car B is traveling at 50 miles per hour. So, the relative speed is 58 - 50 = 8 miles per hour.

Car A needs to cover a distance of 20 miles (the initial distance between the two cars) plus an additional 8 miles (to be 8 miles ahead of Car B). Therefore, Car A needs to cover a total distance of 20 + 8 = 28 miles.

To calculate the time it takes for Car A to cover this distance, we divide the total distance by the relative speed:

Time = Distance / Speed = 28 miles / 8 miles per hour = 3.5 hours

Therefore, it will take Car A 3.5 hours to overtake and drive 8 miles ahead of Car B.

dolorrem · Answer

Why do we divide 8 by relative speed and not by A's own speed?

Bunuel · Answer

We divide by the  relative speed  because Car A is not closing the gap at its full 58 mph. Car B is also moving forward at 50 mph, so the distance between them shrinks only at the difference of their speeds, 58 - 50 = 8 mph.

The total gap Car A needs to cover is 20 miles (to catch up) + 8 miles (to get ahead) = 28 miles.

Time = distance/relative speed = 28/8 = 3.5 hours.

Answer: E.

KarishmaB · Answer

Also, check this video. It will help you understand when to use relative speed: https://youtu.be/wrYxeZ2WsEM

totaltestprepNick · Answer

E https://www.youtube.com/watch?v=3P89xuSgY1U Nick Slavkovich, GMAT/GRE tutor with 20+ years of experience tutoring@totaltestprep.net

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