Question 1182486: A twin engine pontoon boat can cross the river in 18 hours when both engines are operating. It takes 27 hours longer for the boat to cross the river using only engine one than it does when using only engine two. How long would it take each engine working alone to power the boat so it can cross the river? Use lowercase variable t for time and write a quadratic equation to model this problem.
Found 3 solutions by josgarithmetic, mananth, ikleyn:
Answer by josgarithmetic(39616)   (Show Source):
Answer by mananth(16946)  (Show Source):
You can put this solution on YOUR website! A twin engine pontoon boat can cross the river in 18 hours when both engines are operating.
it crosses 1/18 of the river in 1 hour
let engine one take x hours to cross
so it crosses 1/x of the river in 1 hour
Engine 1 takes 27 hours more (x+27)
it crosses 1/(x+27) of the river in 1 hour
1/x + 1/(x+27) = 1/18
multiply equation by x(x+27)*18
18(x+27) +18x = x(x+27)
18x+486 +18x = x^2 + 27x
x^2-9x -486=0
(x-27)(x+18)=0
x= 27 hours engine 1
Answer by ikleyn(52776)  (Show Source):
You can put this solution on YOUR website! .
This problem is posed INCORRECTLY.
As it is worded, printed, posted and presented, it is Physically WRONG.
It is Physically wrong, since in real life situation, the rate of work of two engines,
in the sense and in the context of this problem, IS NOT the sum of rates
of individual engines, due to non-linear nature of a drag force. *)
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*) The Physics fact, well known to any Mechanical engineer.
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