Asmall jet can fly 1,435 miles in 5 hours with a tailwind but only 1,215 miles in 5 hours into a headwind. find the speed of the jet in still air and the speed of the wind.

Speed of Jet in Still Air = 265 miles per hour

Speed of Wind = 22 miles per hour

Step-by-step explanation:

Let x be speed of jet

and c be speed of wind

We know D = RT, where

D is distance

R is rate

T is time

For first leg:

1435 miles in 5 hours, the rate is:

Rate = 287 mph

For second leg:

1215 miles in 5 hours, the rate is:

Rate = 243 mph

So 287 is with wind and 243 against wind, thus we can write:

x + c = 287

x - c = 243

Adding gives us:

2x = 530

x = 265 miles per hour [still rate]

Speed of wind:

x + c = 287

265 + c = 287

c = 22 miles per hour [speed of wind]