Question

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

Answer 1

`7(1)/(3)\text{ weeks}`

Explanation:

Given,

Total distance have to stretch =
`16(1)/(2)` km,

Also, the distance repaired by workers each week =
`2(1)/(4)` km,

Thus, the number of weeks required to repair whole distance

`=\frac{\text{Total distance have to stretch}}{\text{Distance repaired in one week}}`

`=(16(1)/(2))/(2(1)/(4))`

`=((33)/(2))/((9)/(4))`

`=(66)/(9)`

`=7(1)/(3)`

Answer 2

Answer: It will take
`7(1)/(3)` weeks to repair this stretch of road.

Explanation:

Since we have given that

Part of road needs repair =
`16(1)/(2)=(33)/(2)`

Part of road worker can repair per week =
`2(1)/(4)=(9)/(4)`

We need to find the number of weeks that it will take to repair this stretch of road.

So, Number of weeks is given by

`(33)/(2)/ (9)/(4)\\\\=(33)/(2)* (4)/(9)\\\\=(66)/(9)\\\\=(22)/(3)\\\\=7(1)/(3)`

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