Question

Flying against the wind, a jet travels 2100 miles in 3 hours. Flying with the wind, the same jet travels 8480 miles in 8 hours. What is the rate of the jet in still air and what is the rate of the wind?

Answer 1

The rate of jet in still air is 880 mph and rate of wind is 180 mph

Solution:

Given that Flying against the wind, a jet travels 2100 miles in 3 hours

Flying with the wind, the same jet travels 8480 miles in 8 hours

To find: rate of the jet in still air and rate of the wind

Let the rate of jet in still air be  "x"  miles per hour and rate of wind be  "y" miles per hour.

against wind speed = x - y mph

with wind speed = x + y mph

We know that,

$speed = \frac{distance}{time}$

$\text{against wind speed }=\frac{2100}{3}=700 \mathrm{mph}$

$\text{with wind speed} =\frac{8480}{8}=1060 \text{ mph}$

Hence we get,

x - y = 700 --- eqn 1

x + y = 1060 --- eqn 2

Add the above two equations,

x - y + x + y = 700 + 1060

2x = 1760

x = 880

From eqn 1 we get,

880 - y = 700

y = 880 - 700 = 180

y = 180

Thus the rate of jet in still air is 880 mph and rate of wind is 180 mph