Car X left Town T traveling at an average speed of 40 miles per hour.

GMATinsight Thanks for this! I had a quick doubt..

When you say Y has to travel 12+23 = 35 miles, why did we not consider the distance that even X travels? A bit confused here.. I got via approximation as below

X travels 12 miles in 18 minutes.

Y starts and both travel at 14 miles (relative speed)

Now from this time, they both meet after (6/7)th of an hour... [Given d=12 and s=14 and hence t=12/14 which is 6/7)

This is the T1 say, and now to calculate remaining time where Y makes that gap of 23 miles, we continue the relative journey.

Over next 1 hour (60 minutes), distance of 14 is created and another 9 is created as follows

60 minutes -- 14 miles
X minutes -- 9 miles

X minutes = (9*60)/14 = 38 odd minutes.

Now we have 38+60+(6/7 of an hour)

98 + 51 minutes which is 149 minutes and hence 150

I solved this question as following:

If car X is 18 minutes ahead of car Y when the latter starts moving, that means that car Y got 12 miles to catch up: 2/3 mpmin x 18 min= 12 miles (40mph=2/3mpmin).

Using the concept of relative speed, it will take car Y : t= 12miles/14mph= 6/7 hours to close the gap and meet car X.

Now car Y is 23 miles ahead of car X.

Car Y is 14 mph faster than car X, or in other words, every hour that goes by car Y gets 14 miles ahead of car X.

Therefore (again using the concept of relative speed), It will take car Y; t=23miles/14mph to create a gap of 23 miles between itself and car X.

Hence the total time it took car Y to catch up to car X and advance it by 23 miles is: (6/7+23/14) hours= (35/14) hours= (35x60/7) minutes= 150 minutes.


Correct answer is E

RahulJain293 I beleive the method followed by GMATinsight is similar to your and my method, he just added the 12 miles to the 23 miles from the start and applied the concept of relative speed at one go (12/14+23/14 is the same thing as 35/14).

Car y left 18 minutes after car x, this distance covered within period

d = 40 x 3/10

= 12 miles.


Car y then travelled 23 miles ahead.

Total distance covered

= 12 + 23

= 35

Effective speed

54 - 40

= 14

Time that will happen

35/14 x 60

= 150 minutes.

GMAT quant instructor, Lagos Nigeria


Posted from my mobile device

why can't we do 35/54 i.e distance / speed to determine time z?

You can’t do 35/54 because 35 miles is not the distance car Y traveled - it’s the extra distance Y traveled over X.

Since both cars are moving, you need to use relative speed (54 - 40 = 14 mph) to calculate how long it takes for Y to gain 35 miles over X.

That’s why time = 35/14 hours = 150 minutes = z.