# Math Help - Related Rates problem...

1. ## Related Rates problem...

A racer can cycle around a circular loop at the rate of 3 revolutions per hour. Another cyclist can cycle the same loop at the rate of 5 revolutions per hour. If they start at the same time (t=0), at what first time are they farthest apart?

2. Originally Posted by derekjonathon
A racer can cycle around a circular loop at the rate of 3 revolutions per hour. Another cyclist can cycle the same loop at the rate of 5 revolutions per hour. If they start at the same time (t=0), at what first time are they farthest apart?
$s = r \cdot \theta$

for cyclist 1, $\theta_1 = 6\pi t$

for cyclist 2, $\theta_2 = 10\pi t$

$s_2 - s_1 = r(10\pi t - 6\pi t) = r(4\pi t)$

farthest distance will be when they are half a circumference apart ( $\pi r$) ...

$t = \frac{1}{4}$ hr