Question

Archimedes tan 3 times as fast as his challenger in fact he ran 60 miles in 3 hours less than it took his challenger to run 32 miles. How fast did each of them run

Answer 1

Explanation:

he ran 3 times as fast.

speed = distance/time

speed × time = distance

time = distance/speed

x = speed of the challenger = x miles/hour

y = time for 32 miles = 32/x

speed of Archimedes = 3x miles/hour.

y - 3 = 60/3x

using the first in the second equation

32/x - 3 = 60/3x

let's multiply both sides by 3x

3×32 - 9x = 60

96 - 9x = 60

-9x = -36

x = 4

so, the challenger ran 4 mph (in other words : he more or less walked a little bit faster),

Archimedes ran 4×3 = 12 mph.