Problem Solving

swerve wrote:Car X and Car Y traveled the same 80-mile route. If Car X took 2 hours and Car Y traveled at an average speed that was 50 percent faster than the average speed of Car X, how many hours did it take Car Y to travel the route?

A. 2/3
B. 1
C. 4/3
D. 8/5
E. 3

There's a nice rule we can use here.

To set up the rule, recognize that if Y travels 2 times as fast as X, then Y's travel time will be 1/2 of X's.
Similarly, if Y travels 3 times as fast as X, then Y's travel time will be 1/3 of X's.
Or if Y travels 1/4 as fast as X, then Y's travel time will be 4 times X's travel time.

In general, if Y travels a/b times as fast as X, then Y's travel time will be b/a of X's travel time.

So, if Y's speed is 50% more than X's speed, we can say that Y travels 1.5 times as fast as X.
In other words, if Y travels 3/2 times as fast as X, which means Y's travel time will be 2/3 that of X's travel time.

Since X's travel time is 2 hours, Y's travel time will be (2/3)(2) = 4/3 = 1 1/3 = C

Cheers,
Brent

Hi swerve,

We're told that Car X and Car Y traveled the same 80-mile route, Car X took 2 hours and Car Y traveled at an average speed that was 50 percent faster than the average speed of Car X. We're asked for the number of hours it took Car Y to travel the route. With a few standard 'math steps', you can answer this question without too much difficulty.

To start, we can calculate Car X's speed using the Distance Formula:
Distance = (Rate)(Time)
80 miles = (Rate)(2 hours)
80/2 = Rate
Rate = 40 miles/hour

Since Car Y's speed was 50% GREATER than Car X's speed, we can now calculate that speed:
(1.5)(40 miles/hour) = 60 miles/hour

Using that speed, we can calculate how long it took Car Y to travel that same distance:
Distance = (Rate)(Time)
80 miles = (60 miles/hour)(Time)
80/60 = Time
Time = 80/60 = 8/6 = 4/3 hours

Final Answer: C

GMAT assassins aren't born, they're made,
Rich

swerve wrote:Car X and Car Y traveled the same 80-mile route. If Car X took 2 hours and Car Y traveled at an average speed that was 50 percent faster than the average speed of Car X, how many hours did it take Car Y to travel the route?

A. 2/3
B. 1
C. 4/3
D. 8/5
E. 3

We are given that Car X traveled 80 miles in 2 hours. Thus, the rate of Car X was 80/2 = 40 mph.

We are also given that Car Y traveled 50% faster than Car X. Thus, Car Y traveled at a rate of 1.5 x 40 = 60 mph.

So, it took Car Y 80/60 = 8/6 = 4/3 hours to travel the same route.

Answer: C