Aprivate jet can fly 1,210 miles against the headwind in the same amount of time it can fly 1,694 miles with a 25 mph tailwind. find the speed of the jet

The speed of the jet is 150 mph

Let a represent the speed of the jet. The speed of the speed of the wind is 25 mph and t represent the time.

Since jet can fly 1,210 miles against the headwind:

a - 25 = 1210/t

a = 1210/t + 25   (1)

It can fly 1,694 miles with a 25 mph tailwind, hence:

a + 25 = 1694/t

a = 1694/t - 25   (2)

From equation 1 and 2:

1210/t + 25 = 1694/t - 25

1694/t - 1210/t = 50

484/t = 50

50t = 484

t = 9.68 hours

a = 1694/t - 25 = a = 1694/9.68 - 25 = 150 mph

Hence the speed of the jet is 150 mph

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Let us assume speed of the Jet = x mph.

We are given speed of wind = 25 mph.

Total speed of the Jet with tailwind = (x+25) mph.

Total speed of the Jet with headwind = (x-25) mph.

We know, relation among time, rate and time is given by formula:

Time = Distance/Speed.

Both times are same.

Therefore,

On cross multiplying, we get

1210(x+25) = 1694(x-25)

1210x + 30250 = 1694x - 42350.

Adding 42350 on both sides,

1210x + 30250+42350 = 1694x - 42350 + 42350.

1210x +72600 = 1694x

Subtracting 1210x from both sides, we get

1210x-1210x +72600 = 1694x -1210x

72600 = 484x.

Dividing both sides by 484, we get

72600/484 = 484x/484.

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