Question

A small plane, flying in the same direction as the wind, travelled 600 km in 2h. The return trip, flying against the wind, took 3 h. Find the speed of the plane and the wind. Can someone please show the full process on how to answer this question?

Answer 1

$\Huge\tt{{\color{purple}{{\underline{AN}}}}{\color{orchid}{{\underline{SW}}}}{\pink{{\underline{ER}}}}{\color{lightpink}{:-}}}$

• Speed of the plane: 250 mph
• Speed of the wind: 50 mph

$\huge\Large\underline\mathtt\purple{Explanation:-}$

Let p = the speed of the plane

and w = the speed of the wind

It takes the plane 3 hours to go 600 miles when against the headwind and 2 hours to go 600 miles with the headwind. So we set up a system of equations.

600 mi / 3hr = p − w

600mi /2hr = p + w

Solving for the left sides we get:

200mph = p - w

300mph = p + w

Now solve for one variable in either equation. I'll solve for x in the first equation:

200mph = p - w

Add w to both sides:

p = 200mph + w

Now we can substitute the x that we found in the first equation into the second equation so we can solve for w:

300mph = (200mph + w) + w

Combine like terms:

300mph = 200mph + 2w

Subtract 200mph on both sides:

100mph = 2w

Divide by 2:

50mph = w

So the speed of the wind is 50mph.

Now plug the value we just found back in to either equation to find the speed of the plane, I'll plug it into the first equation:

200mph = p - 50mph

Add 50mph on both sides:

250mph = p

So the speed of the plane in still air is 250mph.