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.
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!