# Two drivers started towards each other at the same time from places 24 km apart, one traveled twice as fast as the other and they met in one hour and 40 minutes, at what rates did they travel?

Aug 6, 2015

They travelled at $\text{9.6 km/h}$ and $\text{4.8 km/h}$, respectively.

#### Explanation:

Right from the start, you know that the distances covered by the two drivers must add up to give 24 km.

Since distance is equal to velocity (in this context, to keep things simple, I'll use speed and ignore the direction of movement) multiplied by time, you can write

${d}_{1} = {v}_{1} \cdot {t}_{1}$

${d}_{2} = {v}_{2} \cdot {t}_{2}$

You also know that both drivers drove for 1 hour and 40 minutes, which is equivalent to

100color(red)(cancel(color(black)("minutes"))) * "1 hour"/(60color(red)(cancel(color(black)("minutes")))) = "1.67 hours"

Another important piece of information given to you is the ratio of their speeds; you know that one travelled twice as fast as the other, so you can say that

${v}_{1} = 2 \cdot {v}_{2}$

${d}_{1} + {d}_{2} = 24$
$\left(2 \cdot {v}_{2}\right) \cdot t + {v}_{2} \cdot t = 24$
$3 \cdot {v}_{2} \cdot t = 24 \implies {v}_{2} = \frac{24}{3 \cdot 1.67} = \textcolor{g r e e n}{\text{4.8 km/h}}$
${v}_{1} = 2 \cdot {v}_{2} = 2 \cdot 4.8 = \textcolor{g r e e n}{\text{9.6 km/h}}$