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

Answer:

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

Step-by-step explanation:    

We have been given that a $16\frac{1}{2}$ km stretch of road needs repairs. Workers can repair $2\frac{1}{4}$ kilometer of road per week.

To find the number of weeks it will take to repair the stretch we will divide $16\frac{1}{2}$ by $2\frac{1}{4}$

$\text{Number of weeks it will take to repair the stretch of road}=16\frac{1}{2}\div 2\frac{1}{4}$

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

$\text{Number of weeks it will take to repair the stretch of road}=\frac{33}{2}\div \frac{9}{4}$

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

$\text{Number of weeks it will take to repair the stretch of road}=\frac{33}{2}\times \frac{4}{9}$

$\text{Number of weeks it will take to repair the stretch of road}=\frac{33*2}{9}$

$\text{Number of weeks it will take to repair the stretch of road}=\frac{11*2}{3}$

$\text{Number of weeks it will take to repair the stretch of road}=\frac{22}{3}$

$\text{Number of weeks it will take to repair the stretch of road}=7\frac{1}{3}$

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