GMAT paper test #13

by **1week2go** Mon Sep 17, 2007 11:14 am

as much as I practice these, I can never get rate questions....

Carl drove from his home to the beach at an average speed of 80 km per hour and returned home by the same route at an average speed of 70 km per hour. If the trip home took 1/2 hour longer than the trip to the beach, how many km did Carl drive each way?

a) 350
b) 345
c) 320
d) 280
e) 240

by **Guest** Mon Sep 17, 2007 3:21 pm

is the answer D?

80t = 70(t +.5)

by **1week2go** Mon Sep 17, 2007 3:40 pm

you got it! Answer is D.

by **RonPurewal** Tue Sep 18, 2007 3:51 am

Guest's setup is correct:
The way there: RATE = 80, TIME = t, DISTANCE = 80t
The way back: RATE = 70, TIME = t + 1/2, DISTANCE = 70(t + 1/2)

Because it's a round trip (same distance there as back), you set the two Distance expressions equal, leading to Guest's equation.

This problem is very amenable to BACKSOLVING: plug the answer choices in and see if they work.
Let's try answer choice C:
* The way there: distance = assumed to be 320, rate = 80, so time = 320/80 = 4 hours
* The way back: distance = assumed to be 320, rate = 70, so time = 320/70 = 4 4/7 hours
* It's not a half-hour difference, so this is the wrong answer.
* The difference is MORE than half an hour, so this choice is TOO LONG of a distance (the longer the distance, the bigger the difference between the two times, since everything is proportional)
Let's try answer choice D:
* The way there: distance = assumed to be 280, rate = 80, so time = 280/80 = 3 1/2 hours
* The way back: distance = assumed to be 280, rate = 70, so time = 280/70 = 4 hours
* It's a half-hour difference, so this is the right answer.