Question

Two planes just took off from Boston, MA. The first plane is traveling 2.5 times as fast as the second plane. After traveling in the same direction for 5 hours, they are787.5 miles apart. What is the average speed of each plane? (Hint: Since they are traveling in the same direction, the distance between them will be the difference oftheir distances.)Yonad

Answer 1

Equations

Let's call

x = average speed of the second plane

Since the first plane goes 2.5 as fast as the second, then:

2.5x = average speed of the first plane

In 5 hours, the first plane has traveled:

5*2.5x = 12.5x (in miles)

And the second plane has traveled:

5*x = 5x (in miles).

Given they travel in the same direction, the distance between them is the difference of their respective distances:

Difference = 12.5x - 5x = 7.5x

We are given that value, thus:

7.5x = 787.5

Dividing by 7.5

x = 787.5 / 7.5 = 105 miles per hour

Then:

2.5x = 2.5 * 105 = 262.5 miles per hour.

Answer:

Average speed of the first plane: 262.5 miles per hour.

Average speed of the second plane: 105 miles per hour.