Malcolm can run a race at a speed of 6 minutes per mile, while Joshua runs at 8 minutes per mile. In a 10-mile race, how many minutes after Malcolm crosses the finish line will Joshua cross the finish line if they start the race together?

20 min

Explanation:

The time to cross the finish line may be found using the speed vs. time equation:

speed = distance / time

From which you can solve for time:

time = distance / speed.

Using the last equation, you can find the difference in the times for Malcolm and Joshua, but, since the speed must be expressed in miles per minutes, and the given data are minutes per mile, first you must convert the data.

Miles per minute is the inverse of minutes per mile, so the corresponding speeds are:

Malcolm's speed: 1 / (6 min/mile) = (1/6) miles/min

Joshua's speed: 1 / (8 min/mile) = (1/8) miles/min

Time for Malcom: 10 miles / [ 1 / (6 miles/min) ] = 10 / (1/6) min = 60 min

Time for Joshua: 10 miles / [ 1 / (8 miles/min) ] = 10 / (1/8) min = 80 min

Difference in times: 80 min - 60 min = 20 min

Hence, Joshua will cross the finish line 20 minutes after Malcolm crosses the finish line.