Q:

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?

Accepted Solution

A:
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] weeksThus, it will take  [tex]7\frac{1}{3}[/tex] weeks to complete the repair of the stretch of road.