Question

it took a small plane 2hr longer to fly 375 mi against the wind than it took the plane to fly the same distance with the wind . The rate of thewind was 25mph . Find the rate of the plane in calm air

Answer 1

First, write out the system of equations based on:
\[Distance = speed \space x \space time\]
With the wind:\[(s+25)t=375\]Against the wind:\[(s-25)(t+2)=375\]
Now you have 2 equations with 2 unknowns. You can solve this using substitution. Solving the first equation for t gets you:
\[t=\frac{375}{s+25}\]
Substitute that into the second equation to get:
\[(s-25)(\frac{375}{s+25}+2)=375\]
Solving for s you get +/- 100mph...and you know the speed is positive so it's just 100mph.

You can now solve for t using the original equations:
\[(100+25)t=375\]\[t = 3 hrs\]
\[(100-25)(t+2)=375\]\[t = 5 hrs\]