Question

A road repair crew spread 2/3 of a ton of gravel evenly over 2 feet of road. How many tons of gravel did they spread on each foot of road?

Write your answer as a fraction or as a whole or mixed number.

tons

Answer 1

To find out how many tons of gravel were spread on each foot of the road, we need to divide the total amount of gravel by the length of the road.

The crew spread \( \frac{2}{3} \) of a ton of gravel over 2 feet of road. Therefore, we perform the following calculation:

\[
\text{Gravel per foot} = \frac{\text{Total gravel}}{\text{Length of road}} = \frac{\frac{2}{3}}{2}
\]

Dividing \( \frac{2}{3} \) by 2 is the same as multiplying \( \frac{2}{3} \) by the reciprocal of 2, which is \( \frac{1}{2} \):

\[
\frac{\frac{2}{3}}{2} = \frac{2}{3} \times \frac{1}{2} = \frac{2 \times 1}{3 \times 2} = \frac{2}{6}
\]

Now, simplify \( \frac{2}{6} \):

\[
\frac{2}{6} = \frac{1}{3}
\]

Thus, the crew spread \(\frac{1}{3}\) of a ton of gravel on each foot of road.

The final answer is:

\[
\frac{1}{3} \text{ tons}
\]