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26 Mar 2025, 00:30
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B
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
35%
(medium)
Question Stats:
78% (02:46) correct
22%
(03:04)
wrong
based on 97
sessions
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When Jacob closes the drain of his bathtub and turns on the cold water spigot, it takes him 3 minutes and 40 seconds to fill the tub completely. If he fills it from the hot water spigot instead, it takes him 5 minutes and 30 seconds to fill it completely. When the drain is open in a completely full bath tub, it takes 11 minutes for the tub to empty. How many minutes will it take Jacob to fill the bathtub with both hot and cold water running simultaneously, if the drain is open and draining at a constant pace ?
A. 2 minutes 12 seconds
B. 2 minutes 45 seconds
C. 3 minutes 30 seconds
D. 3 minutes 52 seconds
E. 4 minutes 15 seconds
A. 2 minutes 12 seconds
B. 2 minutes 45 seconds
C. 3 minutes 30 seconds
D. 3 minutes 52 seconds
E. 4 minutes 15 seconds
26 Mar 2025, 01:09
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Let the total capacity of the bathtub be 1 unit of water.
Define the flow rates for each source in units per minute**.
The individual filling rates
- Cold water spigot fills the tub in 3 minutes 40 seconds = 11/3 minutes
→ Rate of cold water: \(\frac{1}{\frac{11}{3}} = \frac{3}{11}\) units/min
- Hot water spigot fills the tub in 5 minutes 30 seconds = 11/2 minutes
→ Rate of hot water: \(\frac{1}{\frac{11}{2}} = \frac{2}{11}\) units/min
Drain rate
- Drain empties a full tub in 11 minutes
→ Drain rate: \(\frac{1}{11}\) units/min
Net filling rate
\(\left(\frac{3}{11} + \frac{2}{11} - \frac{1}{11} \right) = \frac{4}{11}\) units/min
Since the bathtub needs **1 unit** of water to be full: \( \text{Time} = \frac{1}{\frac{4}{11}} = \frac{11}{4} = 2.75 \) minutes
Option B - 2 min 45 sec
Define the flow rates for each source in units per minute**.
The individual filling rates
- Cold water spigot fills the tub in 3 minutes 40 seconds = 11/3 minutes
→ Rate of cold water: \(\frac{1}{\frac{11}{3}} = \frac{3}{11}\) units/min
- Hot water spigot fills the tub in 5 minutes 30 seconds = 11/2 minutes
→ Rate of hot water: \(\frac{1}{\frac{11}{2}} = \frac{2}{11}\) units/min
Drain rate
- Drain empties a full tub in 11 minutes
→ Drain rate: \(\frac{1}{11}\) units/min
Net filling rate
\(\left(\frac{3}{11} + \frac{2}{11} - \frac{1}{11} \right) = \frac{4}{11}\) units/min
Since the bathtub needs **1 unit** of water to be full: \( \text{Time} = \frac{1}{\frac{4}{11}} = \frac{11}{4} = 2.75 \) minutes
Option B - 2 min 45 sec
26 Mar 2025, 01:58
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Cold water spigot = 3min 40 secs = 11/3 min
Rc = 3/11
Hot water spigot = 5min 30 secs = 11/2 min
Rh = 2/11
Drain = 11min
Rd = 1/11
Net Rate, R = 3/11 + 2/11 - 1/11 = 4/11
Time taken = 1/R = 11/4 min = 2min 45sec
Rc = 3/11
Hot water spigot = 5min 30 secs = 11/2 min
Rh = 2/11
Drain = 11min
Rd = 1/11
Net Rate, R = 3/11 + 2/11 - 1/11 = 4/11
Time taken = 1/R = 11/4 min = 2min 45sec
Bunuel
