Question

1. a holding pond in the back lot currently has 320 gallons of water in it. water is being pumped from a nearby river at 7.5 gallons per minute. at this rate, approximately how long would it take to fill the holding pond that has a 4000 - gallon capacity?

a. 7 hours and 50 minutes
b. 8 hours and 10 minutes
c. 8 hours and 30 minutes
d. 8 hours and 50 minutes

Explanation:

Step1: Find the amount of water to pump

The pond has a 4000 - gallon capacity and currently has 320 gallons. So the amount of water to pump is \(4000 - 320=3680\) gallons.

Step2: Calculate time in minutes

The pumping rate is 7.5 gallons per minute. Time (in minutes) \(t=\frac{3680}{7.5}\approx490.67\) minutes.

Step3: Convert minutes to hours and minutes

There are 60 minutes in an hour. Divide 490.67 by 60: \(490.67\div60 = 8\) hours with a remainder. \(0.67\times60\approx40\)? Wait, no, wait. Wait, 7.5 gallons per minute. Wait, maybe I made a mistake. Wait, let's recalculate. Wait, 4000 - 320 is 3680. 3680 divided by 7.5. Let's do 3680 ÷ 7.5. Multiply numerator and denominator by 2: 7360 ÷ 15 ≈ 490.67 minutes. Now, 490.67 minutes: 490 ÷ 60 = 8 hours (8×60 = 480 minutes), and 490.67 - 480 = 10.67 minutes, approximately 10 minutes? Wait, no, the options: let's check again. Wait, maybe the problem is to fill from 320 to 4000, so 3680 gallons. 3680 / 7.5 = 490.666... minutes. 490.666... minutes. 490.666 ÷ 60 = 8 hours and (0.666×60) ≈ 40 minutes? Wait, no, the options are a.7h50m, b.8h10m, c.8h30m, d.8h50m. Wait, maybe I miscalculated the amount to pump. Wait, maybe the pond is empty? No, the problem says "currently has 320 gallons" and "4000 - gallon capacity", so we need to pump 4000 - 320 = 3680. Wait, 7.5 gallons per minute. Let's do 3680 ÷ 7.5. Let's compute 7.5 × 490 = 7.5×400 + 7.5×90 = 3000 + 675 = 3675. So 3680 - 3675 = 5 gallons left. So 490 minutes is 8 hours and 10 minutes (since 8×60 = 480, 490 - 480 = 10). Ah, so 490 minutes is 8 hours and 10 minutes. Wait, 7.5×490 = 3675, which is 5 less than 3680, but approximately, 490 minutes is 8 hours and 10 minutes. So the answer is b? Wait, no, the options: b is 8 hours and 10 minutes. Wait, but let's check again. Wait, maybe the problem is to fill the pond from 0? But the problem says "currently has 320 gallons". Wait, maybe the question is misread. Wait, the problem says "how long would it take to fill the holding pond that has a 4000 - gallon capacity" – maybe "fill" means from empty? But it says "currently has 320 gallons". This is confusing. Wait, let's check the options. Let's assume that maybe the 320 is a typo, or maybe we need to fill 4000 gallons. Then 4000 / 7.5 ≈ 533.33 minutes, which is 8 hours and 53 minutes, close to d. But the problem says "currently has 320 gallons". So 4000 - 320 = 3680. 3680 / 7.5 ≈ 490.67 minutes. 490.67 minutes is 8 hours (480 minutes) and 10.67 minutes, so approximately 8 hours and 10 minutes. So the answer is b? Wait, but let's check the calculation again. 7.5 gallons per minute. In 8 hours (480 minutes), we pump 7.5×480 = 3600 gallons. We need 3680 gallons. So 3680 - 3600 = 80 gallons more. 80 / 7.5 ≈ 10.67 minutes. So total time is 8 hours and 10.67 minutes, approximately 8 hours and 10 minutes. So the answer is b. 8 hours and 10 minutes.

Answer:

b. 8 hours and 10 minutes