Speed/Distance

vaibhav101 wrote: ↑

Wed Jun 06, 2018 8:48 am

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

A 350
B 345
C 320
D 280
E 240

STRATEGY: As with all GMAT Problem Solving questions, we should immediately ask ourselves, Can I use the answer choices to my advantage?
In this case, we can easily test the answer choices.
In fact, since travel time = distance/rate, the speeds of 70 and 80 kmh would need to work nicely with the distance.
When I scan the answer choices, I see that many of them wouldn't work nicely with 70 and 80 kmh, which means I probably won't need to test many answer choices.
So let's start testing values.

APPROACH #1: Testing answer choices
I'm going to start by testing the to answer choices that are divisible by 70 kmh
(A) 350
Travel time the beach = distance/rate = 350/80 = 35/8 = 4 3/8 hours
Travel time home = distance/rate = 350/70 = 5 hours
In this case, the difference between the two travel times = 5 - 4 3/8 = 5/8 hours.
Since we need the time difference to equal 0.5 hours, we can eliminate answer choice A.

(D) 280
Travel time the beach = distance/rate = 280/80 = 28/8 = 7/2 = 3.5 hours
Travel time home = distance/rate = 280/70 = 4 hours
In this case, the difference between the two travel times = 4 - 3.5 = 0.5 hours.
Perfect!
Answer: D


APPROACH #2: Algebra
Since the travel time going home was 0.5 hours longer than the travel time going to the beach, we can start with the following word equation:
(travel time going home) - (travel time to beach) = 0.5

Let d = the distance from home to beach
Since time = distance/rate, we can plug in the given values to get: (d/70) - (d/80) = 0.5
To eliminate the fractions, multiply both sides of the equation by 560 to get: 8d - 7d = 280
Simplify: d = 280

Answer: D