Question

On a 1 mile track, Runner A has made 18 laps in the time it took Runner B to make 8 laps. If Runner A is running 5 mph faster than Runner B, how fast is each of them running?

Answer 1

Runner A is running at 9 mph while runner B is running at 4 mph

Explanation:

From online values, 4 laps make 1 mile.

We are told Runner A has made 18 laps in the time it took Runner B to make 8 laps.

This means that runner A has run in mile; 18/4 = 4.5 miles

While runner B has run in miles; 8/4 = 2 miles

Runner A is running 5 mph faster than Runner B, thus speed of runner A is;

V_b + 5 while speed of runner B is V_b.

We know that; time = distance/speed

Thus;

t_a = 4.5/(V_b + 5)

t_b = 2/V_b

Since the times are equal from the question, then;

4.5/(V_b + 5) = 2/V_b

Cross multiply to get;

4.5V_b = 2(V_b + 5)

4.5V_b = 2V_b + 10

4.5V_b - 2V_b = 10

2.5V_b = 10

V_b = 10/2.5

V_b = 4 mph

Since V_a = V_b + 5

Thus, V_a = 4 + 5 = 9 mph

Runner A is running at 9 mph while runner B is running at 4 mph