Question

Doug, who runs track for his high school, was challenged to a race by his younger brother, matt. Matt started running first, and doug didn’t start running until matt had finished a quarter-mile lap on the school track. Doug passed matt as they both finished their sixth lap. If both boys ran at a constant speed, with doug running 2 miles an hour faster than matt, what was matt’s speed?.

Answer 1

The speed of Matt is 10 mph.

Doug runs 2 miles an hour faster than Matt, so let Matt’s speed equal x miles per hour. Then Doug’s speed equals x + 2 miles per hour. Each lap is one-quarter of a mile, so Doug runs 1.5 miles in the time it takes Matt to run 1.25 miles.

Rate of Matt is x

Rate of Dough is (x + 2)

Time taken by Matt is 1.25/x

Time taken by Dough is 1.25/(x + 2)

Distance covered by Matt is 1.25

Distance covered by Dough is 1.5

Dough and  Matt  took the same amount of time from the time Doug started, so make an equation by setting the two times in the chart equal to each other, and then solve for x:

            $\frac{1.5}{(x + 2)}$ = $\frac{1.25}{x}$

              1.5x = 1.25(x + 2)

              1.5x = 1.25x + 2.5

           0.25x = 2.5

                   x = 10

So Matt ran at 10 miles per hour.

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