Respuesta :
Answer:
It will take [tex]7\frac{1}{3}[/tex] weeks to complete the repair of the stretch of road.
Step-by-step explanation:
Given:
Length of the roads that need repairs = [tex]16\frac{1}{2}\ km[/tex]
Length of the road workers can repair in a week = [tex]2\frac{1}{4}\ km[/tex]
To find the number of weeks will it take to repair this stretch of road.
Solution:
Unit rate of workers to repair roads = [tex]2\frac{1}{4}\ km[/tex] per week.
Total length of the roads to repair = [tex]16\frac{1}{2}\ km[/tex]
The number of weeks it will take to repair [tex]16\frac{1}{2}\ km[/tex] of road by workers can be given as:
⇒ [tex]\frac{16\frac{1}{2}\ km}{2\frac{1}{4}\ km}[/tex]
In order to divide mixed numbers, we convert them first to fractions.
⇒ [tex]\frac{\frac{33}{2}} {\frac{9}{4}}[/tex]
To divide fractions, we take reciprocal of the divisor and replace division with multiplication:
⇒ [tex]\frac{33}{2}\times \frac{4}{9}[/tex]
⇒ [tex]\frac{22}{3}[/tex]
We reconvert the fraction to mixed number.
⇒ [tex]7\frac{1}{3}[/tex] weeks
Thus, it will take [tex]7\frac{1}{3}[/tex] weeks to complete the repair of the stretch of road.
