Question

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

a) 7 weeks
b) 6 1/2 weeks
c) 8 weeks
d) 7 1/2 weeks

Answer 1

It will take approximately 7 1/4 weeks to repair the road.

Step-by-step explanation:

To find out how many weeks it will take to repair a 16 1/2 kilometer stretch of road by workers who repair 2 1/4 kilometers per week, we can divide the total distance by the distance repaired per week. First, we convert 16 1/2 kilometers to a mixed number, which is 16 km + 1/2 km = 16 km + 1/2 km * (4/2) = 16 km + 2/4 km = 16 km + 1/4 km = 16 1/4 km. Next, we divide 16 1/4 km by 2 1/4 km/week. To divide mixed numbers, we convert them to improper fractions. 16 1/4 km = (16 x 4 + 1)/4 km = 65/4 km. 2 1/4 km/week = (2 x 4 + 1)/4 km/week = 9/4 km/week. Now, we can divide 65/4 km by 9/4 km/week: (65/4 km) ÷ (9/4 km/week) = 65/4 km x 4/9 km/week = 65/9 weeks. So it will take approximately 7 1/4 weeks to repair the road.