Word Problems - solving with systems

Question

A jetliner can travel 1700 mi from Fargo, ND, to Phoenix, AZ, in 4 hr with a tailwind; but it takes 3 hr to travel 975 mi from Phoenix to Boise, ID, into the same wind. Determine both the wind speed and the air speed (speed in still air) of the plane

Answer 1

R is the speed of the plane

s is the spped of the wind

1700 = 4( R+s) = 4R+4s

975 = 3( R-s) = 3R-3s

Adding them together:

2675 = 7R + s <--- labels this equation ALPHA

3 * eq1 and 4 * eq2

======================

5100 = 12R + 12s

3900 = 12R - 12s

Adding them together:

9000 = 24R

R = 9000/24 = 3000/8 = 1500/4 = 750/2 = 375

Per equation ALPHA:

2675 = 7R + s

2675 = 7 (375) + s

2675 = 2625 + s

s = 50

Answer 2

Two equations for the two situations are:

V = velocity

W=wind speed

975 = (V - W)3 Flying against the wind for 3 hours

1700 = (V+W)4 Fling with the wind for 4 hours

Solving yields: V = 375 mph W = 50 mph

(I solved graphically...it was easier)