Chapter A.8, Problem 45AYU

To determine

To find: How far from the start will Mike pass Dan? How long does it take?

Answer to Problem 45AYU

Mike passes Dan $\frac{1}{3}$ mile from the start. 2 min to the time Mike started to run.

Explanation of Solution

Given:

Mike can run the mile in 6 minutes and Dan can run in 19 minutes. If Mike gives Dan a head start of 1 minute, how far from the start will Mike pass Dan? How long does it take?

Calculation:

Let $t=\text{ M’s}$ running time then $\left(t+1\right)=\text{ D’s}$ running time.

When $\text{M}$ catches $\text{D}$, they will have run the same distance.

$\frac{1}{6}t=\frac{1}{9}\left(t+1\right)$

Multiply both side by 18, we get

$3t=2\left(t+1\right)$

$3t-2t=2$

$t=2$

$t=2$ minutes for $\text{M}$ to catch $\text{D}$.

Therefore mike passes Dan $\frac{1}{3}$ mile from the start. 2 min to the time Mike started to run.