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

Unit rate in metric tons per hour = 1.17

Step-by-step 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(1)/(4) =(5*4+1)/(4) =(21)/(4)`

Time taken in hours
`=4(1)/(2) =(4*2+1)/(2) =(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{(21)/(4)} {(9)/(2)} =1.17`

Answer 2

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(1)/(4)` metric tons of dirt from a construction site in
`4(1)/(2)` hours.

A construction company can remove
`(21)/(4)` metric tons of dirt from a construction site in
`(9)/(2)` hours.

Now

`(21)/(4)\ metric\ tons= (9)/(2)\ hours`

`unit\ rate\ in\ metric\ tons\ per\ hour = \frac{(21)/(4)} {(9)/(2)}`

`unit\ rate\ in\ metric\ tons\ per\ hour = (21* 2)/(4* 9)`

`unit\ rate\ in\ metric\ tons\ per\ hour = (7)/(6)\ metric\ tons`

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