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.
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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