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# rate change

Posted on 2013-10-31
Medium Priority
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Question 1
Two ships, the Elsa and the Violet, have collided. Fuel immediately starts leaking from the Elsa into the sea.

The captain of the Elsa estimates that at the time of the collision his ship has 6075 litres of fuel on board and he also forecasts that it will leak into the sea at a rate of t2/5
litres per minute, where t is the number of minutes that have elapsed since the collision.

a.  At this rate how long, in minutes, will it take for all the fuel from the Elsa to leak into the sea?

I dont get the answer as I need to integrate dv/dt? Why cant I just use the rate  to use to find.
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Question by:jagguy
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LVL 84

Expert Comment

ID: 39613825
the rate is a function of t so
integral(0..m: (t 2)/5 dt) = 6075
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Author Comment

ID: 39613850
yes i know but I dont understand why you need to take the integral because the rate is given and isnt that enough?
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LVL 84

Expert Comment

ID: 39613872
Yes, it's enough, and setting its integral from t=0 equal to the litres of fuel on board at t=0 is a solution method
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Author Comment

ID: 39613884
I am confused , if you have  tank  2 litre that empties  2 litres per minute then after 1 minute the tank empties . You dont take the integral for such a problem as the rate is enough
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Author Comment

ID: 39613916
This doesnt make sense, the answer is t=45. so if t=45 then the rate is 405 l/min it empties and it takes only 15 mins to empty at this rate.
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LVL 84

Expert Comment

ID: 39613964
The rate is not constant.  It is a function of t
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LVL 37

Accepted Solution

TommySzalapski earned 2000 total points
ID: 39614136
t is time elapsed so far, not total time. So when t=0 at the time of the collision, no fuel is leaking out, then it starts leaking slowly and get's faster.
It's a very simple formula so the integral will be simple. You could short cut it by using the average rate, but that wouldn't help you learn the concepts.

Total time is not 45 minutes unless you missed something in the question
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Author Comment

ID: 39615470
The answers says 45 mins and that is the time it takes to empty out.

k, The rate is not constant so that is why you cant simply use the rate divide it in the total litres.
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LVL 84

Expert Comment

ID: 39615507
sounds like the rate was t^2/5, not t*2/5
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