The plane was travelling 164 mph.
We begin with the formula d=rt, where d is distance, r is rate (speed) and t is time. The time is the same for both vehicles, so we will solve the formula for t:
d=rt
Divide both sides by r:
d/r = t
We know that the time is the same for both vehicles so this sets up a proportion:
d/r = d/r
The car travels 80 miles at an unknown speed, x:
80/x = d/r
The plane travels 400 miles at 160 mph faster than the unknown speed:
80/x = 400/(x+160)
Cross multiply:
80(x+160) = 400*x
80x + 1280 = 400x
Subtract 80x from both sides:
80x + 1280 - 80x = 400x - 80x
1280 = 320x
Divide both sides by 320:
1280/320 = 320x/320
4 = x
The car travels at 4 mph; the plane travels at 4+160 = 164 mph.
