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10 Feb 2026, 23:24
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C
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Difficulty:
45%
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Question Stats:
77% (03:05) correct
23%
(02:39)
wrong
based on 65
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A ship is 180 kilometers from shore when it springs a leak, letting in 3 metric tons of water every 8 minutes. The ship will sink once it takes in 90 metric tons of water. The ship’s pumps can remove 12 metric tons of water per hour. What speed should the ship maintain to reach the shore exactly as it reaches the point of sinking?
A. 15 km/h
B. 18 km/h
C. 21 km/h
D. 24 km/h
E. 27 km/h
A. 15 km/h
B. 18 km/h
C. 21 km/h
D. 24 km/h
E. 27 km/h
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11 Feb 2026, 00:25
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Net water intake (Ton per min) = 3/8 - 12/60 = 3/8 -1/5 = 7/40.
Time to to reach point of sinking, T= 90/(7/40) min = (90 x 40)/(7 x60) hr = 60/7 hr
Speed = 180 /T = 180 x 7/60 kmph = 21 kmph
Time to to reach point of sinking, T= 90/(7/40) min = (90 x 40)/(7 x60) hr = 60/7 hr
Speed = 180 /T = 180 x 7/60 kmph = 21 kmph
Bunuel
11 Feb 2026, 01:33
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Understanding the Problem:
Think of this as a "race against time" problem. The ship is filling with water, but the pumps are fighting back. We need to find how long the ship can stay afloat, then figure out how fast it needs to go to cover 180 km in that time.
Step 1: Find how fast water is coming IN
The leak lets in 3 tons every 8 minutes.
To convert to tons per hour:
Rate = (3 tons / 8 minutes) × 60 minutes = 22.5 tons per hour
Step 2: Find the NET rate of water accumulation
Water coming IN: 22.5 tons/hour
Water being pumped OUT: 12 tons/hour
Net rate = 22.5 - 12 = 10.5 tons per hour
Even with pumps working, the ship still gains 10.5 tons of water every hour.
Step 3: Find how long until the ship sinks
The ship sinks after taking in 90 tons of water.
Time = Total capacity ÷ Net rate = 90 ÷ 10.5
Let's simplify: 90 ÷ 10.5 = 900 ÷ 105 = 60/7 hours (approximately 8.57 hours)
Step 4: Calculate the required speed
The ship needs to travel 180 km in 60/7 hours.
Speed = Distance ÷ Time = 180 ÷ (60/7) = 180 × (7/60) = 1260/60 = 21 km/h
Key Principle:
In problems with competing rates (filling vs emptying), always calculate the NET rate first. Make sure all units match (convert minutes to hours when needed).
Answer: C (21 km/h)
Think of this as a "race against time" problem. The ship is filling with water, but the pumps are fighting back. We need to find how long the ship can stay afloat, then figure out how fast it needs to go to cover 180 km in that time.
Step 1: Find how fast water is coming IN
The leak lets in 3 tons every 8 minutes.
To convert to tons per hour:
Rate = (3 tons / 8 minutes) × 60 minutes = 22.5 tons per hour
Step 2: Find the NET rate of water accumulation
Water coming IN: 22.5 tons/hour
Water being pumped OUT: 12 tons/hour
Net rate = 22.5 - 12 = 10.5 tons per hour
Even with pumps working, the ship still gains 10.5 tons of water every hour.
Step 3: Find how long until the ship sinks
The ship sinks after taking in 90 tons of water.
Time = Total capacity ÷ Net rate = 90 ÷ 10.5
Let's simplify: 90 ÷ 10.5 = 900 ÷ 105 = 60/7 hours (approximately 8.57 hours)
Step 4: Calculate the required speed
The ship needs to travel 180 km in 60/7 hours.
Speed = Distance ÷ Time = 180 ÷ (60/7) = 180 × (7/60) = 1260/60 = 21 km/h
Key Principle:
In problems with competing rates (filling vs emptying), always calculate the NET rate first. Make sure all units match (convert minutes to hours when needed).
Answer: C (21 km/h)
