Car A is 20 miles behind Car B, which is traveling in the opposite

Question

Car A is 20 miles behind Car B, which is traveling in the opposite direction along the same route as Car A. Car A is traveling at a constant speed of 65 miles per hour and Car B is traveling at a constant speed of 55 miles per hour. Approximately how many minutes will it take for Car A and B be on a 20 miles distance from each other again?

(a) 10
(b) 200
(c) 20
(d) 45
(e) 36

(a) 10
 (b) 200
 (c) 20
 (d) 45
 (e) 36

EgmatQuantExpert · Answer

Given

• Car A is 20 miles behind Car B, which is traveling in the opposite direction along the same route as Car A.
 o The behind word is creating confusion here. If you look at the image, then this statement indicates that this is case 2.
o In that case, they will never be 20 miles apart unless they are moving in a circular direction.

• Car A is traveling at a constant speed of 65 miles per hour and Car B is traveling at a constant speed of 55 miles per hour.

To Find

• Minutes it will take for Car A and B be on a 20 miles distance from each other again.
 o The only possible way to understand this problem when they are initially in the position as case 1 and then they are in the position as in case 2.

Approach and Working Out

• It is given that both the distances are 20 miles.
 o Relatively, they are traveling 40 miles. 
• Their relative velocity is 65 + 55 = 120 miles/hour 
 o They will take  \frac{40}{120}  hours =  \frac{1}{3}  hours or 20 minutes.

Correct Answer: Option D

stne · Answer

Hi BrendaMSL ,
Welcome to GMAT club. Here is the solution to your question.

Now cars are 20 miles apart. For them to be 20 miles apart again, first cars must meet and then travel away from each other, until they are 20 miles apart again.

Let  t  be the time in which they meet then we can form this equation  \hspace{1mm}  55t + 65t = 20 \Rightarrow \hspace{2mm} t = \frac{1}{6}  or 10 minutes

Now let  x  be the time in which they are 20 Miles apart traveling away from each other, again we can form the equation  55x + 65x = 20 \Rightarrow x = \frac{1}{6}  or 10 minutes.

So total time to be 20 Miles apart again 10 +10 = 20 Minutes

Hope it's clear.

hemantbafna · Answer

A and B are 20 miles away
First they have to cover the 20 miles distance between them and then 20 miles more in total 40 miles.

When travelling in opposite direction we need to add the speeds.
C

Therefore time=40/120*60=20 mins

Posted from my mobile device

MathRevolution · Answer

Car A and car B are traveling in opposite directions.

Opposite direction ( Case I: Towards each other and Case II: Away from each other).

Car A is 20 miles behind Car B - If case II is applied first then both cars will never meet. Hence Case I is to be considered first when they are 20 miles apart and then case II in which they are again 20 miles apart.

Total distance : 20 + 20 = 40 miles
Total relative speed : 65 + 55 = 120 miles per hour.

Time taken:  \frac{Distance}{ Speed}

Time taken:  \frac{40 }{ 120}

Time taken:  \frac{1}{3}  hours  i.e., 20 minutes

Answer C

drwharton3900 · Answer

Try Backsolving Pick OPtioon C 20 +20 = 40 (Total Distance ) Total Speed 65+55=120 40/120 =1/3 ~20 min

v12345 · Answer

This can be easily solved with the help of relative velocity,
Relative v = 65 - (-55) = 120 miles per hour
Distance = 40 miles
Time = 40/120 = 1/3 hr = 20 min

Hence, OA is (C).

joe123x · Answer

Miles per minute for A = 65/ 60 
13/12
Miles per minutes for B = 55/60
11/12

Both together they cover 24/12= 2miles per minute.

It takes 10 minutes for them to cover 20miles, and then another 10 minutes to be 20miles away from each other.

Posted from my mobile device

bumpbot · Answer

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Car A is 20 miles behind Car B, which is traveling in the opposite

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Car A is 20 miles behind Car B, which is traveling in the opposite

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