Solving a distance, rate, time problem.

Question

Flying against the wind, an airplane travels 2550 kilometers in 3 hours. Flying with the wind, the same plane travels 10,000 kilometers in 8 hours.

What is the rate of the plane in still air and what is the rate of the wind?

Rate of the plane in still air:

Rate of the wind:

Answer 1

So, these used to really confuse me. Turns out it's actually pretty simple.

Now, let's say I'm in a canoe and I can row 2 kph. If I'm in a river with a current of 8 kph, I'm going to travel 2 + 8 = 10 kph going downstream, and after 2 hours I'll have travelled 20 kilometers.

But if I try to row upstream, I'm going to end up going backward! 2 - 8 = -6 kph, so I'd be headed backward at 6 kph. I guess that could be a good workout or something, and after one hour, I'd be 6 kilometers behind where I started.

d = rt

Let p = the rate of the plane in still air and let w = the rate of the wind.

3(p - w) = 2550

8(p + w) = 10,000

p - w = 850

p + w = 1250

2p = 2100

p = 1050 kph

1050 + w = 1250

w = 200 kph