Question

A plane traveled 768 miles to Cairo and back. The trip there was with the wind. It took 8 hours. The trips back was into the wind. The trip back took 16 hours. What is the speed of the plane in still air? What is the speed of the wind?

Answer 1

Let's call the speed of the plane in still air "p" and the speed of the wind "w". We can use the formula distance = rate x time, or d = rt, to create two equations based on the given information:

Equation 1: 768 = (p + w) x 8 (the trip to Cairo with the wind)
Equation 2: 768 = (p - w) x 16 (the trip back from Cairo against the wind)

We can simplify these equations by dividing both sides by the time and then solving for "p":

Equation 1: 96 = p + w
Equation 2: 48 = p - w

We can solve this system of equations by adding the two equations together:

96 + 48 = 2p
144 = 2p
p = 72

So the speed of the plane in still air is 72 mph. We can substitute this value back into one of the original equations to solve for the speed of the wind:

96 = 72 + w
w = 24

Therefore, the speed of the wind is 24 mph.