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A ship 156 km away from the shore springs a leak, which admits 7/3 metric tons of water in 13/2 min, but the pumps throw out 15 metric tons of water in 1 hour.70 metric tons would suffice to sink the ship.find the average rate of sailing so that she may just reach the shore as she begins to sink.

(a)14.5 (b)15 (c)18 (d)20

Attempted soln:

In 13/2 min water admitted = 7/3 metric Tons

Therefore in 1 hr=60 min water admitted = $(7/3)*(2/13)*60=280/13$ metric tons

In 1hr water accumulated=$(280/13)-15=85/13$ metric ton.

Therefore 70 metric ton accumulated in $(13/85)*70=(13*14)/17 = 182/17$ hours

Therefore speed should be = $156*(17/182)=14.57$ km/h.

I am getting the answer as 14.57. However, the given answer is 15 km/h.

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    I get the answer ${102 \over 7} \approx 14.57$, perhaps the answer is rounded? – 2017-01-25
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    It would seem an error in the book. copper.hat and I agree with you. – 2017-01-25
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    Yes I too get the same answer. But if we round off, the answer should be closer to 14.5 than 15 – 2017-01-25
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    Thank you so much gentlemen. :) – 2017-01-25
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    14.57 > 14.5 so the boat would sink just a tiny bit off shore. No good. 15> 14.57 so the boat would make it to shore. Just barely. Good. 20 >> 14.57 so the boat would make it to shore with plenty of time to spare. " so that she may just reach the shore as she begins to sink" is vague and there are wiggle-room but 15 is the most appropriate answer.... But It's an irritating question as by *math* standards, 14.57 which is closest to 14.5 really should be the technical and "math conceptually" correct answer. – 2017-01-25

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You are correct in everything except you semantic "jail-house lawyering" ability to nitpick. Which ... in not mathematics.

The answer is $14.\overline{571428}$ which as you point out rounds closest to $14.5$.

BUT reread the question: "so that she may just reach the shore as she begins to sink"

$14.5 < 14.\overline{571428}$ so at $14.5$ the boat will sink before she gets to shore. She'll be very close (we can calculate exactly how close but I'm too lazy) but she will she will be off shore and sink.

So no good.

At this point it may be sensible to ask: "well, why should we bother calculating the speed needed to just barely make it. Wouldn't it just be better to play it safe and go as fast as she can? If the boat can go 20 kph, shouldn't it?"

Good question.

Anyway, rest assure your math was just fine. In the long run that's what matters for you. (As long as I'm never on your boat.)

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Also as long as we are nitpicking: "find the average rate of sailing" implies there is just one. Obviously 14.6 or 15.25 also qualify. Heck. Try heading in at exactly 14.5715 and watch the boat sink just as the first person steps ashore! That'd be something!

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    Understood your point :) Thankyou – 2017-01-25
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    Rough estimating at 14.5 kph she'll be a little over 2 km out to see when she sinks. I think. – 2017-01-25
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    You ability to make things understand is commendable. Thank you sir. I wasn't nitpicking. I just didn't think from your viewpoint, until you explained it in the comment so very well. Right we should also consider practical physical aspects instead of just relying on mathematical data. Thank you sir :) – 2017-01-25
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    You may not have been nitpicking, but *I* was! I didn't get it at first and I was typing a completely different comment about the assumption of rounding, when I realized that you can't round down, only up. To be honest, I don't think this is a fair math question. – 2017-01-25