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Two cars, Car1 and Car2 move towards each other from X and Y

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Two cars, Car1 and Car2 move towards each other from X and Y

by BTGmoderatorLU » Wed May 16, 2018 3:34 pm
Two cars, Car1 and Car2 move towards each other from X and Y respectively with respective speeds of 20 m/s and 15 m/s. After meeting each other Car1 reaches Y in 10 seconds. In how many seconds does Car 2 reach X starting from Y?

A. 15.5 sec
B. 8.4 sec
C. 33.6 sec
D. 31.11 sec
E. 16.8 sec

The OA is D.

X--------------------------------------|----------------------------Y
Car A(20mps)------------------------->P<---------------Car B(15mps)

Let 2 cars meet each other at point P in t seconds.

Car1 covers distance= 20t. Car2 covers distance=15t. So, total distance XY= 35t.

From P, Car 1 reaches onto Y in 10 secs. So it covers 15t further.
so, 15t/20 = 10
So t=40/3 sec and total distance = (35*40)/3
Hence Car2 will cover total distance in (35*40)/(3*15) = 31.11 sec approx.

Can anyone explain another way to solve this PS question? Thanks!
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by Vincen » Fri May 18, 2018 4:25 am
Hello BTGmoderatorLU.

I would solve as you did it.

Car 1 ----- 20 m/s
Car 2 ----- 15m/s

Let be t the time that took both Cars to meet each other. Hence,

Car 1 has covered 20t miles.
Car 2 has covered 15t miles.

This implies that their combined distance is 35t.

Since Car 1 reaches Y 10 seconds after meeting Car 2, then we can rewrite the total distance from X to Y as: $$35t=20t+20\cdot10\ \Leftrightarrow\ \ \ 15t=200\ \ \Leftrightarrow\ \ t=\frac{40}{3}\text{seconds}.$$ Therefore, the total distance from X to Y is $$35t=35\cdot\frac{40}{3}=\frac{1400}{3}m.$$ Since Car 2 goes at 15 m/s then the time needed to go from Y to X is equal to $$T=\frac{d}{v}=\frac{\frac{1400}{3}}{15}=\frac{1400}{45}=\frac{280}{9}\approx31.11.$$ Hence, the correct answer is the option D.

I hope it can help you.
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by Jeff@TargetTestPrep » Fri May 18, 2018 10:35 am
BTGmoderatorLU wrote:Two cars, Car1 and Car2 move towards each other from X and Y respectively with respective speeds of 20 m/s and 15 m/s. After meeting each other Car1 reaches Y in 10 seconds. In how many seconds does Car 2 reach X starting from Y?

A. 15.5 sec
B. 8.4 sec
C. 33.6 sec
D. 31.11 sec
E. 16.8 sec
We can let the time it takes the cars to meet as t and let the total distance = 20(t + 10) = 20t + 200 and create the equation:

20t + 15t = 20t + 200

15t = 200

t = 200/15 = 40/3

So the total distance is 20(40/3) + 200 = 800/3 + 600/3 = 1400/3 meters.

Thus,at a rate of 15 meters per second, it takes Car 2 (1400/3)/15 = 1400/45 = 280/9 = 31.11 seconds to travel from X to Y.

Answer: D

Jeffrey Miller
Head of GMAT Instruction
[email protected]

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