Question

this must be the hardest question ever because no one knows what to do xD MY BRAIN IS FRIED from studying allllll day and this is a word problem please helllpppp!!

Answer 1

sorry kro I'm trying to help someone

Answer 2

Let the speed of the boat in still water be x miles per hour. Then the speed up river will be (x - 6) mph and the speed down river will be (x + 6) mph. Now we can write an equation putting the time for the upstream trip plus the time for the downstream trip equal to 9 hours, as follows:
\[\large \frac{22.5}{x-6} + \frac{22.5}{x+6}=9\ ...........(1)\]
Equation (1) can be rearranged to form a quadratic, which can then be solved to find the value of x (the required speed of the boat in the lake).

Answer 3

umm i don't think I'm understanding this correctly i got 45/(x-6)(x+6)

Answer 4

We the two fractions on the left hand side of (1) are added, we get:
\[\large \frac{22.5(x+6)+22.5(x-6)}{(x-6)(x+6)}=9\ .............(2)\]

Answer 5

so it cancels out and you have 45

Answer 6

And (2) reduces to:
\[\large \frac{45x}{x^{2}-36}=9\ ..........(3)\]

Answer 7

okay i get that except for the right side

Answer 8

The 9 on the right side is the 9 hours for the total journey up the river and back down the river.

Answer 9

okay what is the .............(1)(2)(3)

Answer 10

The equations (1), (2) and (3) are a progression leading ultimately to a quadratic to be solved, which is as follows:
\[\large x^{2}-5x-36=0\ ..........(4)\]

Answer 11

okay so we plug in the values

Answer 12

Not really. We have to solve the quadratic in equation (4) by factoring it.

Answer 13

i got 9 and -4

Answer 14

Good work! The minimum still water speed required for the boat is therefore 9 miles per hour.

Answer 15

what about the -4?

Answer 16

The -4 is an impossible solution. It is therefore discarded.

Answer 17

okay thank you kro for your patience and for helping me(:

Answer 18

You're most welcome :)