Question

An airplane flies from Houston to Denver with a tailwind that increases its normal speed by 60 mph. On the return trip, the plan must fly against this wind, which decreases its normal speed by the same amount. The flight from Houston takes 2.4 hours and the return trip takes 2.76 hours. How far is it from Houston to Denver?

Answer 1

Given data:

The speed of the plane when it flies from Houston to Denver is a=(x+60) mph.

The speed of the plane when it flies from denver to Houston is b=(x-60) mph.

The time taken by the plane when it flies from Houston to Denver is t=2.4 h.

The time taken by the plane when it flies from Denver to Houston is t'=2.76 h.

Assume the distance bewteen Houston to Denver is y.

The distance when the plane flies from Houston to Denver is,

y=(x+60)2.4

y=2.4x+144.......(I)

The distance when the planne flies from Denver to Houston is,

y=2.76(x-60)

y=2.76x-165.6......(II).

Equate both the equations.

2.4x+144=2.76x-165.6

309.6=2.76x-2.4x

x=860 mph

The distnace between Houston to Denver is,

y=(860+60)2.4

=2,208 miles.

Thus, the distance between Houston and Denver is 2,208 miles.