Two friends live 3 miles apart along the same road. If they walk toward each other at rates that differ by half mile per hour and meet 24 minutes later, how fast is each person walking

Answer: their speeds are 3.5mph and 4 mph

Step-by-step explanation:

Since both friends live 3 miles apart along the same road, by the time they meet, they would have covered 3 miles.

Let x represent the speed of the slower friend.

If differ by half mile per hour, it means that the speed of the faster friend is (x + 0.5) mph

They meet after 24 minutes (24/60 = 0.4 hours)

Distance = speed * time

Distance covered by the slower friend in 0.4 hours is

x * 0.4 = 0.4x

Distance covered by the faster friend in 0.4 hours is

0.4 (x + 0.5) = 0.4x + 0.2

Since the total distance is 3 miles, then

0.4x + 0.4x + 0.2 = 3

0.8x = 3 - 0.2 = 2.8

x = 2.8/0.8

x = 3.5 mph

The speed of the faster friend is

3.5 + 0.5 = 4 mph