# Two cars were 539 miles apart and started traveling towards each other on the same road at the same time. One car is going at 37 miles per hour, the other is going at 61 miles per hour. How long did it take for the two cars to pass each other?

May 27, 2016

The time is $5 \frac{1}{2}$ hours.

#### Explanation:

Apart from the speeds given, there are two extra pieces of information which are given, but are not obvious.

$\Rightarrow$The sum of the two distances travelled by the cars is 539 miles.
$\Rightarrow$ The time taken by the cars is the same.

Let $t$ be the time taken by the cars to pass each other.

Write an expression for the distance travelled in terms of $t$.

Distance = speed x time

${d}_{1} = 37 \times t$ and ${d}_{2} = 61 \times t$

${d}_{1} + {d}_{2} = 539$

So, $37 t + 61 t = 539$

$98 t = 539$

$t = 5.5$

The time is $5 \frac{1}{2}$ hours.