Throughout last week, water was leaking from a certain tank at a constant rate of \frac{1}{4} gallon per hour, and 14 gallons of water were added to the tank every day at 1 o'clock in the afternoon. If there were 32 \frac{3}{4} gallons of water in the tank at 2 o'clock last Tuesday afternoon, at what time last week were there 46 \frac{3}{4} gallons of water in the tank? A. 2 o'clock Wednesday afternoon B. 1 o'clock Thursday morning C. 6 o'clock Thursday morning D. 10 o'clock Thursday evening E. 2 o'clock Friday morning

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Throughout last week, water was leaking from a certain tank at a const

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patpathaha

Joined: 28 May 2025

Last visit: 09 Mar 2026

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25 Dec 2025, 13:03

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Water go out at 1/4 gallon per hour => for x hours, water go out x/4 gallon

Tuesday @ 2 PM
- It's at 32+3/4 gallon

Wednesday 1 PM
- It's 23 hours from Tuesday @ 2 PM
- So the amount of water got out is 23/4, or 5+3/4 gallon
- So the amount of water left is 32+3/4 - 5+3/4 = 27 gallon
- 14 new gallon of water was added, so 27 + 14 = 41 gallon
Since the water keep getting out, the amount of water will always be less than 41 gallon for the next 24 hours. We finding the time when it reaches 46 gallons, so it won't happening in the next 24 hours.

Thursday 1 PM
- It's 24 hours from Wednesday 1 PM
- So the amount of water got out is 24/4, or 6 gallon
- So the amount of water left is 41 - 6 = 35 gallon
- 14 new gallon of water was added, so 35 + 14 = 49 gallon

Finding the hours
- The ending is 46+3/4 gallon
- That means the amount of water got out is 49 - 46+3/4 = 9/4 gallon
- Hours it has passed since Thursday 1 PM is 9 hours (9/4 divided by 1/4)
- So 1 PM + 9 hours = 10 PM, on Thursday

Hope this helps