Question

A twin-engine plane flies 380 mi in the same amount of time it takes a single-engine plane to fly 220 mi. The rate of the twin-engine plane is 80 mph faster than the rate of the single-engine plane. Find the rate of the single-engine plane.

Answer 1

The rate of the single engine plane is 110 mph.

Explanation:

Let the rate of single engine plane be n mph,

And the rate of twin engine plane will be n + 80 mph.

We know that, distance = speed x time.

Then, for twin engine plane

380 = (n + 80) x time taken

`\text{{time taken}} = (380)/(n+80)`

And, for single engine plane

220 = n x time taken

`\text{{time taken}} = (220)/(n)`

It is given that, both planes took same time.

Then,
`(380)/(n +80) = (220)/(n)`

380n = 220n + 220 x 80

380n – 220n = 17600

160n = 17600

`n =(17600)/(160)`

n = 110

Hence, the rate of the single engine plane is 110 mph.