*** I will give you a medal if you help/answer ***
The speed of the current in a river is 6 mph. A ferry operator who works that part of the river is looking to buy a new boat for his business. Every day, his route takes him 22.5 miles against the current and back to his dock, and he needs to make this trip in a total of 9 hours. He has a boat in mind, but he can only test it on a lake where there is no current. How fast must the boat go on the lake in order for it to serve the ferry operator’s needs?

Question

*** I will give you a medal if you help/answer ***
The speed of the current in a river is 6 mph.  A ferry operator who works that part of the river is looking to buy a new boat for his business. Every day, his route takes him 22.5 miles against the current and back to his dock, and he needs to make this trip in a total of 9 hours. He has a boat in mind, but he can only test it on a lake where there is no current. How fast must the boat go on the lake in order for it to serve the ferry operator’s needs?

anonymous · Answer

Take 22.5 miles divide by 9 hrs to find speed on water without current and add 6mph to the speed ?

anonymous · Answer

is this for sure how you do it.. ??

anonymous · Answer

i got 8.5

anonymous · Answer

thats how I would do it. think of it this way, u add 6 mph to the boat and it cancels out the river current, so your remaining speed is the speed needed to cross the river 22.5 miles in 9 hrs

anonymous · Answer

@jim_thompson5910

jim_thompson5910 · Answer

let x = speed of the boat in still water

now let's find the distance equation for the boat when it goes against the current

d = rt

d = (x - 6)*t ... 
the speed gets slowed down against the current, so that's why it drops to x-6


22.5 = (x-6)*t

now solve for t

22.5/(x-6) = t

t = 22.5/(x-6)

So it takes 22.5/(x-6) hours to go 22.5 miles upstream 

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Now let's find the equation when the boat goes with the current


d = rt

d = (x + 6)*t
the speed gets faster with the current, so that's why it bumps up to x+6

22.5 = (x + 6)*t

22.5/(x + 6) = t

t = 22.5/(x + 6)

So it takes 22.5/(x+6) hours to go 22.5 miles downstream

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You want the two times to add to 9 hours, so...

 22.5/(x-6)  +   22.5/(x + 6)   = 9

solve this for x to get your answer

anonymous · Answer

how do i solve for x ?

anonymous · Answer

find a LCM to cancel out the equations ? or what ?

jim_thompson5910 · Answer

good, multiply everything by the LCD to clear out the fractions

jim_thompson5910 · Answer

the LCD is (x-6)(x+6)

anonymous · Answer

so i would multiply everything by 135 ?

anonymous · Answer

oh

jim_thompson5910 · Answer

no (x-6)(x+6)

anonymous · Answer

im confused ?

anonymous · Answer

so i take 22.5(x-6)(x+6)

jim_thompson5910 · Answer

start with the first fraction

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