Question

An airliner can travel 750 miles in the same amount of time that it takes a private plane to travel 300 miles. The speed of the airliner is 60 mph more than twice the speed of the private plane. What is the speed of the airliner?

Answer 1

120mph.

Explanation:

let s = the speed of the private plane

then

(2s+60) = the speed of the commercial airliner

:

Write a time equation; time = dist/speed

300%2Fs = 750%2F%28%282s%2B60%29%29

cross multiply

750s = 300(2s+60)

750s = 600s + 18000

750s - 600s = 18000

150s = 18000

s = 18000/150

s = 120 mph is the speed of the private plane

then

2(120) + 60 = 300 mph is speed of the commercial airliner

:

:

Check this find the actual time for each

300/120 = 2.5 hrs

750/300 = 2.5 hrs, confirms our solutions

Find the speed of each aircraft

The ratio of the distances flown is 750:300 = 5:2. Since the times are the same, the ratio of the speeds is 5:2. So let the two speeds be 5x and 2x.

The speed of the airliner in mph is 60 more than twice the speed of the private plane:

5x+=+2%282x%29%2B60

5x+=+4x%2B60

x+=+60

The speeds of the two aircraft are 5x = 300mph and 2x = 120mph.