Question

A jet can fly at a rate of 480 mi/h in calm air. Traveling with the wind, the plane flew 1560 mi in the same amount of time it took to fly 1320 mi against the wind. Find the rate of the wind.

Answer 1

Let the Rate of the Wind be : W mi/h

Given : The Jet can fly at a rate of 480 mi/h

⇒ Travelling with the Wind, Jet flies with a speed of (480 + W) mi/h

⇒ Travelling against the Wind, Jet flies with a speed of (480 - W) mi/h

Given : The Jet Travels 1560 Miles, Travelling with the Wind

Let us calculate How much time the Jet takes to Travel 1560 Miles

In One Hour : The Jet travels a Distance of (480 + W) Miles

⇒ The Jet travels a Distance of 1560 Miles in :
`[(1560)/(480 + W)]\;Hours`

Given : The Jet Travels 1320 Miles, Travelling against the Wind

Let us calculate How much time the Jet takes to Travel 1320 Miles

In One Hour : The Jet travels a Distance of (480 - W) Miles

⇒ The Jet travels a Distance of 1320 Miles in :
`[(1320)/(480 - W)]\;Hours`

Given : Time taken to fly 1560 Miles with the Wind = Time taken to fly 1320 Miles against the Wind.

⇒
`(1560)/(480 + W) = (1320)/(480 - W)`

⇒ 1560(480 - W) = 1320(480 + W)

⇒ (1560 × 480) - 1560W = (1320 × 480) + 1320W

⇒ 1560W + 1320W = (1560 × 480) - (1320 × 480)

⇒ 2880W = 480(240)

⇒ 288W = 48(240)

⇒ 72W = 12(240)

⇒ 6W = 240

⇒ W = 40

⇒ The Rate of Wind is 40 mi/h