Respuesta :
Answer:
[tex]7\frac{1}{3}[/tex] weeks.
Step-by-step explanation:
We have been given that a [tex]16\frac{1}{2}[/tex] km stretch of road needs repairs. Workers can repair [tex]2\frac{1}{4}[/tex] kilometer of road per week.
To find the number of weeks it will take to repair the stretch we will divide [tex]16\frac{1}{2}[/tex] by [tex]2\frac{1}{4}[/tex]
[tex]\text{Number of weeks it will take to repair the stretch of road}=16\frac{1}{2}\div 2\frac{1}{4}[/tex]
Upon converting our mixed fractions into improper fractions we will get,
[tex]\text{Number of weeks it will take to repair the stretch of road}=\frac{33}{2}\div \frac{9}{4}[/tex]
Dividing a fraction with another fraction is same as multiplying the 1st fraction with the reciprocal of second fraction.
[tex]\text{Number of weeks it will take to repair the stretch of road}=\frac{33}{2}\times \frac{4}{9}[/tex]
[tex]\text{Number of weeks it will take to repair the stretch of road}=\frac{33*2}{9}[/tex]
[tex]\text{Number of weeks it will take to repair the stretch of road}=\frac{11*2}{3}[/tex]
[tex]\text{Number of weeks it will take to repair the stretch of road}=\frac{22}{3}[/tex]
[tex]\text{Number of weeks it will take to repair the stretch of road}=7\frac{1}{3}[/tex]
Therefore, it will take [tex]7\frac{1}{3}[/tex] weeks to repair the stretch of the road.
