Question

A construction company takes 1 7/8 hours to remove 3 1/2 metric tons of dirt from a construction site. What is the unit rate in metric tons per hour? Write your answer as a fraction or a mixed number in simplest form.

Answer 1

To find the unit rate of dirt removed per hour, divide the total amount of dirt by the number of hours and simplify. The unit rate is 28/15, or 1 13/15 metric tons per hour.

Step-by-step explanation:

To find the unit rate in metric tons per hour, we will divide the total metric tons of dirt removed by the number of hours it took to remove it. The company removes 3 1/2 metric tons of dirt in 1 7/8 hours. First, we need to convert the mixed numbers to improper fractions to make the division easier:

3 1/2 becomes 7/2 metric tons

1 7/8 becomes 15/8 hours

Now, calculate the unit rate:

Divide 7/2 by 15/8 to find the rate per hour.

To do this, multiply 7/2 by the reciprocal of 15/8, which is 8/15.

The calculation will be (7/2) * (8/15) = 56/30.

Simplify the fraction by dividing both the numerator and the denominator by their greatest common divisor, which is 2, resulting in 28/15.

The unit rate is 28/15 metric tons per hour, or simplified further, 1 13/15 metric tons per hour.