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A ship 156 km from the shore springs a leak which admits 2.5 metric tons of water In \(6 \frac{1}{2}\) minutes. A quantity of 68 metric tons would suffice to sink it, but the pumps can throw out 15 metric tons in an hour. The average rate of sailing so that it just reaches the shore as it begins to sink should be
A. 60 kmph B. 18 kmph C. 15 kmph D. 12 kmph E. 10 kmph
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OA is B The water is adding at the rate of 2.5 metric ton @ 6.5 min i.e. 0.3846 ton in 1 min The water is been pumped out at the rate of 15 metric tons @ 60 minutes i.e. 0.25 ton in 1 min So total water adding into ship is +0.3846-0.25=0.1346 ton/min 68 metric tons is enough to sinc ship. So 68 metric tons will fill in 68/0.1346=505.2 minutes which is 8.42 hours. The ship was about to sync when it reached shore. So distance=speed*time 156/8.42=18.52 approx 18 minutes So OA is B
A ship 156 km from the shore springs a leak which admits 2.5 metric tons of water In \(6 \frac{1}{2}\) minutes. A quantity of 68 metric tons would suffice to sink it, but the pumps can throw out 15 metric tons in an hour. The average rate of sailing so that it just reaches the shore as it begins to sink should be
A. 60 kmph B. 18 kmph C. 15 kmph D. 12 kmph E. 10 kmph
Given: A ship 156 km from the shore springs a leak which admits 2.5 metric tons of water In \(6 \frac{1}{2}\) minutes. A quantity of 68 metric tons would suffice to sink it, but the pumps can throw out 15 metric tons in an hour.
Asked: The average rate of sailing so that it just reaches the shore as it begins to sink should be
Leak admits water @ rate of = 2.5 metric tons / 6.5 mins = 2.5 * 60 /6.5 metric tons / hour = 5*60/13 = 300/13 = 23 1/13 metric tons /hour Pump can throw out water @rate of = 15 metric tons/hour
Effective leak if pump is working = 23 1/3 - 15 = 8 1/3 = 25/3 metric tons/hour
A quantity of 68 metric tons would suffice to sink it.
Time available before sinking = 68 / (25/3) = 68*3/25 = 8.16 hours Distance from shore = 156 km
Average speed required to reach shore before sinking = 156 / 8.16 = 19.11 kmph
Hi Bunuel Please check whether question is correct.
Archived Topic
Hi there,
This topic has been closed and archived due to inactivity or violation of community quality standards. No more replies are possible here.
Still interested in this question? Check out the "Best Topics" block above for a better discussion on this exact question, as well as several more related questions.