Nancy and Audrey set out to cover a certain distance by foot. Nancy walks half the distance and runs half the distance, but Audrey walks half the time and runs half the time. Nancy and Audrey walk and run at the same rate.
Who will reach the destination first (or will it be a tie)?
Answer
Audrey will reach the destination first.
Suppose they cover 12 miles, both walking at a rate of 2 miles per hour and running at a rate of 6 miles per hour. Use the formula:rt = d (rate X time = distance) to find each person’s time.
Nancy (walks half the distance and runs half the distance):
2t = 6 miles, so t = 3 hr. walking
6t = 6 miles, so t = 1 hr. running
t = 4 hours total time
Audrey (walks half the time and runs half the time):
2(0.5t) + 6(0.5t) = 12 miles
t + 3t = 12
4t = 12
t = 3 hours total time