algebra word problem

Question

The 4200 km trip from New York to San Francisco take 6 h flying against the wind but only 5 h returning. Find the speed of the plane in still air and the speed of the wind.

Answer 1

d = rt

The wind speed is added going downwind and subtracted going upwind. If a bird can fly 3 mph, it's going 8 mph with a 5-mph wind but backward 2 mph against the wind.

4200 = 6(p - w)

4200 = 5(p + w)

700 = p - w

840 = p + w

2p = 1540

p = 770 mph

700 = 770 - w

w = 70 mph

Answer 2

I will assume for this problem that the San Francisco - NY journey encounters the same wind but in the opposite(positive) direction.

for this problem the distance traveled is the same so you must find two equations and set them equal to the other. For the purposes of this problem x will be the speed the plane flies(with no wind). Y will be the wind.

6(x - y) = 5(x + y) = 4200

6x - 6y = 5x + 5y

For this problem you can take one of the equations in terms of the 4200 and substitute but the easiest way is to multiply one of the equations so that you can add the linear equations and isolate a variable.

5x + 5y = 4200 multiplied by 6/5 is 6x + 6y = 5040

6x + 6y = 5040

6x - 6y = 4200

+

————————

12x = 9240

x = 770

plug in x to one of the equations and you find y = 70