guy123 wrote:
Carl drove from his home to the beach at an average speed of 80 kilometers per hour and returned home by the same route at an average speed of 70 kilometers per hour. If the trip home took 1/2 hour longer than the trip to the beach, how many kilometers 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) = 0.5Let d = the distance from home to beach
Since
time = distance/rate, we can plug in the given values to get:
(d/70) - (d/80) = 0.5To eliminate the fractions, multiply both sides of the equation by 560 to get:
8d - 7d = 280Simplify:
d = 280Answer: D