Question

A 16\dfrac1216 2 1 ? kilometer stretch of road needs repairs. Workers can repair 2\dfrac142 4 1 ? kilometer of road per week. How many weeks will it take to repair this stretch of road?

Answer 1

`7(1)/(3)` weeks.

Step-by-step explanation:

We have been given that a
`16(1)/(2)` km stretch of road needs repairs. Workers can repair
`2(1)/(4)` kilometer of road per week.

To find the number of weeks it will take to repair the stretch we will divide
`16(1)/(2)` by
`2(1)/(4)`

`\text{Number of weeks it will take to repair the stretch of road}=16(1)/(2)/ 2(1)/(4)`

Upon converting our mixed fractions into improper fractions we will get,

`\text{Number of weeks it will take to repair the stretch of road}=(33)/(2)/ (9)/(4)`

Dividing a fraction with another fraction is same as multiplying the 1st fraction with the reciprocal of second fraction.

`\text{Number of weeks it will take to repair the stretch of road}=(33)/(2)* (4)/(9)`

`\text{Number of weeks it will take to repair the stretch of road}=(33*2)/(9)`

`\text{Number of weeks it will take to repair the stretch of road}=(11*2)/(3)`

`\text{Number of weeks it will take to repair the stretch of road}=(22)/(3)`

`\text{Number of weeks it will take to repair the stretch of road}=7(1)/(3)`

Therefore, it will take
`7(1)/(3)` weeks to repair the stretch of the road.