Question

A jet travels 2384 miles against a jetstream in 4 hours and 2984 miles with the jetstream in the same amount of time. What is the rate of the jet in still air and what is the rate of the jetstream?

Answer 1

The velocity of jet in still air u = 671
`(mi)/(hr)`

The velocity of air v = 75
`(mi)/(hr)`

Explanation:

Let the velocity of jet = u
`(mi)/(hr)`

the velocity of stream = v
`(mi)/(hr)`

Jet travels 2384 miles against a jet stream in 4 hours.

Upstream velocity of the jet is given by,

⇒ u - v =
`(2384)/(4)`

⇒ u - v = 596
`(mi)/(hr)` --------- ( 1 )

Jet travels 2984 miles along a jet stream in 4 hours.

⇒ Downstream velocity of the jet is given by,

⇒ u + v =
`(2984)/(4)`

⇒ u + v = 746
`(mi)/(hr)` ----------- ( 2 )

by adding equation 1 & 2 we get,

⇒ 2 u = 1342

⇒ u = 671
`(mi)/(hr)`

This is the velocity of jet in still air.

Put this value of u in equation 2 we get,

⇒ 671 + v = 746

⇒ v = 75
`(mi)/(hr)`

This is the velocity of air.