Jim can run 5 miles per hour on level ground on a still day

Jim can run 5 miles per hour on level ground on a still day. One windy day, he runs 10 miles with the wind, and in the same amount of time runs 4 miles against the wind. What is the rate of the wind?

Solution

Make this chart DISTANCE RATE TIME With wind Against wind >>...he runs 10 miles with the wind, and in the same amount of time runs 4 miles against the wind...<< Fill in the two distances DISTANCE RATE TIME With wind 10 Against wind 4 Let the rate of the wind be x miles per hour. So when running with the wind, his rate is increased by x mph. So we add x to his rate of 5mph and get 5+x mph, so fill that rate in: DISTANCE RATE TIME With wind 10 5+x Against wind 4 When running against the wind, his rate is decreased by x mph. So we subtract x from his rate of 5mph and get 5-x mph, so fill that rate in: DISTANCE RATE TIME With wind 10 5+x Against wind 4 5-x Now use TIME = DISTANCE/RATE to fill in the two times: DISTANCE RATE TIME With wind 10 5+x 10/(5+x) Against wind 4 5-x 4/(5-x) >>>...in the same amount of time...<< This says the two times are equal: 10 4