Question

A construction company can remove 5 1/4 metric tons of dirt from a construction site in 4 1/2 hours. What is the unit rate in metric tons per hour.

Answer 1

ANSWER

Find out the what is the unit rate in metric tons per hour.

To prove

Unit Rate is the ratio of two measurements in which the second term is unit .

i.e here used for 1 hour.

As given

A construction company can remove $5\frac{1}{4}$ metric tons of dirt from a construction site in $4\frac{1}{2}$ hours.

A construction company can remove $\frac{21}{4}$ metric tons of dirt from a construction site in $\frac{9}{2}$ hours.

Now

$\frac{21}{4}\ metric\ tons= \frac{9}{2}\ hours$

$unit\ rate\ in\ metric\ tons\ per\ hour = \frac{\frac{21}{4}} {\frac{9}{2}}$

$unit\ rate\ in\ metric\ tons\ per\ hour = \frac{21\times 2}{4\times 9}$

$unit\ rate\ in\ metric\ tons\ per\ hour = \frac{7}{6}\ metric\ tons$

The unit rate in metric tons per hour is 1.17 metric tons(approx).

Answer 2

Answer:

 Unit rate in metric tons per hour = 1.17

Explanation:

 A construction company can remove 5 1/4 metric tons of dirt from a construction site in 4 1/2 hours.

 Dirt removed $=5\frac{1}{4} =\frac{5*4+1}{4} =\frac{21}{4}$

 Time taken in hours $=4\frac{1}{2} =\frac{4*2+1}{2} =\frac{9}{2}$

 Unit rate in metric tons per hour = Dirt removed in metric tons/ Time taken in hours for that.

      Unit rate in metric tons per hour $=\frac{\frac{21}{4}} {\frac{9}{2}} =1.17$