How do i solve this word problem

Question

with a head wind, plane traveled 1000 miles in 4 hours. with the same wind as a tail wind, the return trip took 3 hours and 20 minutes. find the plane's speed and the wind speed?

 

Answer 1

Let x = speed of plane in still air

       y = speed of wind

 

Distance = (speed)(time)

 

speed with a head wind  = x - y, so 1000 = (x - y)(4)

 

                                              Therefore,  4x - 4y = 1000

 

{3 hr 20 min = 3 hr + 1/3 hr = 10/3 hr}

 

 speed with a tail wind = x + y, so 1000 = (x + y)(10/3)

 

                                                      Therefore, 10x + 10y = 3000

 

We have 4x -    4y = 1000

               10x + 10y = 3000

 

divide 4x - 4y = 1000 by 4 to get x - y = 250

divide 10x + 10y = 3000 by 10 to get x + y = 300

 

We have:      x - y = 250

                      x + y = 300

 

Adding the equations, we obtain 2x = 550

                                                            x = 275 and 275 + y = 300

                                                                                             y = 25

 

The speed of the plane in still air is 275 mph and the speed of the wind is 25 mph.