Question

1. there was a blizzard. snow was falling at a rate of 4 ½ inches per hour. if the snow kept accumulating at the same rate, how long would it take for 5 feet of snow to accumulate?

proportion with units
work + solution

Explanation:

Step1: Convert units

First, convert 5 feet to inches. Since 1 foot = 12 inches, 5 feet = \(5\times12 = 60\) inches.

Step2: Set up proportion

Let \(t\) be the time in hours. The rate is \(4\frac{1}{2}=\frac{9}{2}\) inches per hour. We set up the proportion: \(\frac{\frac{9}{2}\text{ inches}}{1\text{ hour}}=\frac{60\text{ inches}}{t\text{ hours}}\)

Step3: Solve for \(t\)

Cross - multiply: \(\frac{9}{2}t=60\times1\)
Then, \(t = 60\div\frac{9}{2}=60\times\frac{2}{9}=\frac{120}{9}=\frac{40}{3}\approx13.33\) hours.

Answer:

The time it takes for 5 feet (60 inches) of snow to accumulate at a rate of \(4\frac{1}{2}\) inches per hour is \(\frac{40}{3}\) hours (or approximately 13.33 hours).