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tafara27
It takes 6hrs longer to cross a channel in a ferryboat when one engine of the boat is usd alone than when a second engine is used alone. Using both engines , the ferryboat can make the crossing in 4hrs .How long would it take each engine , working alone ,to power the ferryboat across the channel

Question

34

tafara27
It  takes 6hrs longer to cross a channel in a ferryboat when one engine of the boat is usd alone than when a second engine is used alone. Using both engines , the ferryboat can make the crossing in 4hrs .How long would it take each engine , working alone ,to power the ferryboat across the channel

hero · Answer

1st engine x
2nd engine x - 6

$\large\frac{x(x-6)}{x + (x - 6)} = 4$

hero · Answer

Solve for x to get time it takes the first engine, then subtract 6 from x to get the second engine time.

anonymous · Answer

Let x be the time it takes the second engine to cross a channel alone.
From the problem narrative, one can derive the following equation.$$\frac{1}{x+6}+\frac{1}{x}=\frac{1}{4} $$The solution for x is
x       =   6 hours
x + 6 = 12 hours

$$\frac{1}{12}+\frac{1}{6}=\frac{1}{4} $$

hero · Answer

That's very nice but solving for x using it my way also produces x = 12, x - 6 = 6

And then using the formula I provided you get:

$\frac{12(12-6)}{12 + 12 - 6}=4$ and $\frac{72}{18}=4$

anonymous · Answer

Yes, you let x be the first engine it seems, so the numeric values are reversed in the solutions.

Don't remember doing "combined rate problems" in school.  When first encountered on this site I memorized the method and have used the form of adding fractions, job/hour(s) since then.

hero · Answer

I used Satellite's 

$\large\frac{M \times N}{M + N} = T$ method which I prefer.