One car travels 30 miles in the same amount of time it takes another car to travel 25 miles. If the second car travels five miles per hour slower, how fast does the second car travel?

Question

The answers are:

A. 15 mph

B. 40 mph

C. 25 mph

D. 30 mph

Answer 1

The only way that all the criteria can be met is if the time is 1 hour.

Car A goes 30 mi in 1 hr = 30 mph

Car B goes 25 mi in 1 hr = 25 mph , or 5 mph slower, as specified.

If "t" was 2 hrs it wouldn't work out.

Car A goes 30 mi in 2 hrs = 15 mph

Car B goes 25 mi in 2 hrs = 12.5 mph (not a difference of 5 mph)

Can also use algebra: A's rate is r_A = 30/t mph; B's rate is r_B = 25/t mph, but r_B = r_A - 5.

So 25/t = 30/t - 5. Mult both sides by t. 25 = 30 - 5t -> -5t = 25 - 30 -> -5t = -5, so t must = 1 hr.and B's rate is 25 mph (answer is C)