
A: 194

Q: Mr. Cawley biked 10 miles in half an hour with the wind at his back. Returning against the wind, the trip was 40 minutes.
On a windless day, how long would it take him to bike the 10 miles?
A: The two equations are both based on d = rt
(although below they are written as t multiplied by the rate).
r = the rate without the wind in mph
w = rate of the wind in mph
First we have to find the r without the wind.
1/2 (r + w) = 10 multiply by 2 r + w = 20
2/3 (r – w) = 10 multiply by 3/2 r – w = 15
2r = 35
r = 17.5
w = 2.5
To find the rate at which he biked the 10 miles, we use d = rt again
10 = 17.5 t
so time = 10/17.5 hours which when we mulitply by 60 to get minutes, our answer is 34 2/7 minutes.