One person runs 2 miles per hour faster than another person. The first person runs 5 miles in th same time the second person runs four miles. Find the speed of each person

Answer 1

F=2+S First is 2mph faster than 2nd.

Ft = 5 speed times time = distance

St =4

F/5 = S/4

(2+S)/5 = S/4

4(2+S) = 5S

4S +8 = 5S

S = 8mph

F 10 mph

First runner ran 5 miles at 10 mph in half an hour 10x1/2 = 5 miles

Second runner ran 4 miles at 8 mph in half an hour 8x 1/2 = 4 miles

Answer 2

You would start with the formula: d=rt distance = rate * time). Since the problem stats a distance and information about the rates, you would rewrite the formula as t = d/r.

For the first person, since they are running a longer distance in the same amount of time, they must be the faster of the two. If the slower person is running at rate r, the faster person is running at rate r + 2.

For the first person, the time they take to run 5 miles is calculated by t = 5 / (r + 2)

For the second person, the time they take to run 4 miles is calculated by t = 4 / r

Since the times are equal, we can set the expressions equal to each other: 5 / (r + 2) = 4 / r.

This makes a proportion, and we can cross multiply to solve it:

5r = 4(r+2)

5r = 4r + 10

r = 10

The first person runs at 10 + 2 or 12 mph and the second person runs at 10 mph