Question

A 16 1/2 kilometer stretch of road needs repairs. Workers can repair 2 1/4 kilometer of road per week. How many weeks will take to repair this stretch of road?

Answer 1

Answer:

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

Step-by-step explanation:

we know that

To find out how many weeks it will take to repair this stretch of road, divide the total length of the road by the workers' rate

so

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

Convert mixed number to an improper fraction

$16\frac{1}{2}\ km=\frac{16*2+1}{2}=\frac{33}{2}\ km$

$2\frac{1}{4}\ km=\frac{2*4+1}{4}=\frac{9}{4}\ km/week$

substitute

$(33/2)/(9/4)=\frac{132}{18}\ weeks$

Convert to mixed number

$\frac{132}{18}\ weeks=\frac{126}{18}+\frac{6}{18}=7\frac{1}{3}\ weeks$