Speed Problem!

Ozlemg 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 the 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) 1 1/3 (D) 1 3/5 (E) 3

There's also 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

Ozlemg 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 the 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) 1 1/3 (D) 1 3/5 (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 route.

Answer: C