Question

A 161216\dfrac12 16 2 1 ? kilometer stretch of road needs repairs. Workers can repair 2142\dfrac14 2 4 1 ? kilometer of road per week. How many weeks will it take to repair this stretch of road?

Answer 1

`\bf\textbf{Number of weeks = }7\tfrac{3}{9}`

Explanation:

`\text{Kilometer of road needed to be repaired = }16\tfrac{1}{2}\\\\\text{Kilometer of road needed to be repaired = }(33)/(2)`

`\text{Kilometer of road repaired by workers in one week = }2\tfrac{1}{4}\\\\\text{Kilometer of road repaired by workers in one week = }(9)/(4)`

`\text{No of weeks required to repair one km of road = }(1)/((9)/(4))=(4)/(9)\\\\\implies\text{No of weeks required to repair }(33)/(2)\text{ km of road = }(9)/(4)*(33)/(2)\\\\\implies (66)/(9)=7\tfrac{3}{9}\text{ weeks}`

Answer 2

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

Explanation:

We have been given that a
`16(1)/(2)` kilometer 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 of road we will divide total length of the stretch by part of the road repaired by workers in one week.

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

Since dividing one fraction by another fraction is same as multiplying the 1st fraction by the reciprocal of 2nd fraction.

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

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

Upon cancelling out GCF of our numerator and denominator we will get,

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

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

`\text{The 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 road.