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:

It will take  $7\frac{1}{3}$ weeks to complete the repair of the stretch of road.

Step-by-step explanation:

Given:

Length of the roads that need repairs = $16\frac{1}{2}\ km$

Length of the road workers can repair in a week = $2\frac{1}{4}\ km$

To find the number of weeks will it take to repair this stretch of road.

Solution:

Unit rate of workers to repair  roads =   $2\frac{1}{4}\ km$ per week.

Total length of the roads to repair = $16\frac{1}{2}\ km$

The number of weeks it will take to repair  $16\frac{1}{2}\ km$ of road by workers can be given as:

⇒ $\frac{16\frac{1}{2}\ km}{2\frac{1}{4}\ km}$

In order to divide mixed numbers, we convert them first to fractions.

⇒ $\frac{\frac{33}{2}} {\frac{9}{4}}$

To divide fractions, we take reciprocal of the divisor and replace division with multiplication:

⇒  $\frac{33}{2}\times \frac{4}{9}$

⇒ $\frac{22}{3}$

We reconvert the fraction to mixed number.

⇒ $7\frac{1}{3}$ weeks

Thus, it will take  $7\frac{1}{3}$ weeks to complete the repair of the stretch of road.