Middle school math question

Question

A boat travels x miles per hour from one island to another in 2.5 hours. The boat travels 5 miles per hour faster on the return trip of 2 hours. What is the distance between the islands?

Answer 1

This problem uses the formula D = RT (distance equals rate times time).

The distance of the 1st trip can be represented by D = 2.5x where 2.5 hours is the time and x is the unknown rate.

The return trip distance is D = 2(x + 5), where time is 2 hours and the rate is five miles per hour faster than the 1st trip. Note that the variable D was used in both cases because the distance of both trips is the same.

Using the substitution method:

2.5x = 2(x+5)

2.5x = 2x + 10

0.5x = 10 [or (1/2)x = 10]

x = 10 / (1/2) = 20 (this is the rate of the boat on the 1st trip)

To find the distance between the islands substitute 20 into either equation for D.

D =2.5(20)= 50 miles

or

D = 2(20 + 5) = 50 miles