Question

jaren is going to fill up his pool after he has completed needed pool repairs. his pool will hold 15,000 gallons of water and fills at 480 gallons per hour.
the following equation is written to represent the situation. 15,000 ÷ 480 = 31.25
which of the following best explains the meaning of 31.25?
a jaren is going to have to wait for 31.25 hours to complete his pool repairs.
b jaren is going to have to spend $31.25 on pool repairs.
c it will take 31.25 hours to fill the pool after jaren has repaired it.
d the repairs will take 31.25 hours to complete.

Explanation:

Step1: Analyze the formula

The formula \(15000\div480 = 31.25\) is based on the relationship \(time=\frac{volume}{flow - rate}\), where the volume of the pool is \(15000\) gallons (the amount of water needed to fill the pool) and the flow - rate is \(480\) gallons per hour (the rate at which the pool is filled).

Step2: Check each option

• Option A: The formula has nothing to do with pool repair time. The problem states "after he has completed needed pool repairs", so this option is wrong.
• Option B: The formula involves volume and flow - rate (gallons and gallons per hour), not money. So this option is wrong.
• Option C: Using the formula \(t=\frac{V}{r}\) (where \(V = 15000\) gallons and \(r=480\) gallons per hour), \(t = 31.25\) hours represents the time to fill the pool. This option is correct.
• Option D: The formula is about filling the pool after repair, not the repair time. So this option is wrong.

Answer:

C. It will take 31.25 hours to fill the pool after Jaren has repaired it.