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

Answer:

$7\frac{1}{3}\text{ weeks}$

Step-by-step explanation:

Given,

Total distance have to stretch = $16\frac{1}{2}$ km,

Also, the distance repaired by workers each week = $2\frac{1}{4}$ km,

Thus, the number of weeks required to repair whole distance

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

$=\frac{16\frac{1}{2}}{2\frac{1}{4}}$

$=\frac{\frac{33}{2}}{\frac{9}{4}}$

$=\frac{66}{9}$

$=7\frac{1}{3}$

Answer 2

Answer: It will take $7\dfrac{1}{3}$ weeks to repair this stretch of road.

Step-by-step explanation:

Since we have given that

Part of road needs repair = $16\dfrac{1}{2}=\dfrac{33}{2}$

Part of road worker can repair per week = $2\dfrac{1}{4}=\dfrac{9}{4}$

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

$\dfrac{33}{2}\div \dfrac{9}{4}\\\\=\dfrac{33}{2}\times \dfrac{4}{9}\\\\=\dfrac{66}{9}\\\\=\dfrac{22}{3}\\\\=7\dfrac{1}{3}$

Hence, it will take $7\dfrac{1}{3}$ weeks to repair this stretch of road.