Puzzle from Fawn Nguyen's puzzles and brainteasers, set 13
Here's one possible way to solve it. Choose some easy numbers for the distance they travel, for the speeds, and for the time in case of Frank.Then just calculate!
Let's say they run 10 miles per hour and walk 5 miles per hour. Let's also say the distance from A to B is 20 miles.
Fred runs half the way. So, Fred runs 10 miles = 1 h, and he walks 10 miles = 2 h. So he takes a total of 3 hours.
Frank runs half the time and walks half the time. Now, we don't know the time, so let it be t. We can write an equation about the total distance:
(distance running) + (distance walking) = 20 miles
(1/2t) * 10 + (1/2t) * 5 = 20
5t + 2.5t = 20
7.5 t = 20
t = 2 2/3 hours
So, Frank is quicker.