Question

Two cars started to move at the same time in the same direction, but one was moving twice as fast as the other. Six hours later, the cars were 204 miles apart. Find the speed of each car.

Answer 1

Let the speed of the slower car be \( x \) miles per hour. Then the speed of the faster car is \( 2x \) miles per hour.

The distance traveled by the slower car in 6 hours is given by:
\[
\text{Distance}_{\text{slower}} = x \times 6 = 6x
\]

The distance traveled by the faster car in 6 hours is given by:
\[
\text{Distance}_{\text{faster}} = 2x \times 6 = 12x
\]

According to the problem, the distance between the two cars after 6 hours is 204 miles. Therefore, we can set up the equation:
\[
\text{Distance}_{\text{faster}} - \text{Distance}_{\text{slower}} = 204
\]
Substituting the expressions for the distances gives:
\[
12x - 6x = 204
\]

Now simplify the left side:
\[
6x = 204
\]

Next, divide both sides by 6:
\[
x = \frac{204}{6} = 34
\]

Thus, the speed of the slower car is:
\[
x = 34 \text{ mph}
\]

The speed of the faster car is:
\[
2x = 2 \times 34 = 68 \text{ mph}
\]

In summary, the speeds of the cars are:
- Slower car: **34 miles per hour**
- Faster car: **68 miles per hour**