Question

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 each way 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?

Answer 1

22.5/(x+6) + 22.5/(x-6) = 9

Answer 2

How did you get that

Answer 3

http://openstudy.com/study#/updates/510045c6e4b00c5a3be6aace

Answer 4

I still don't understand ......

Answer 5

@thomaster

Answer 6

@phi

Answer 7

what ?

Answer 8

hold on while i get someone

Answer 9

@goformit100

Answer 10

i don't know sorry. that is as much as i could help! Ask an ambassador for help.

Answer 11

if river current pushes 6mph ---> that way
then when you're going --> you'll be pushed by the river
while going <-- you'll be pulled

if you let your speed be represented by " x "
then your speed going --> way would be x+6
and your speed going <-- way would be x-6

follow so far? :)

Answer 12

yes

Answer 13

then distance divided by speed = time
so since distance = 22.5miles twice (back and forth)
and you have different speeds going back and forth

22.5 22.5
----- + ----- = 9
(x+6) (x-6)

Answer 14

ok so where do we go from there?

Answer 15

solve for x...
I multiplied both sides by (x+6)(x-6)
to get
22.5(x-6) + 22.5(x+6) = 9(x+6)(x-6) then use distributive property

Answer 16

9(b^2-36) = 9b^2 - 324

Answer 17

mmm yep
22.5(x-6) + 22.5(x+6) = 9(x+6)(x-6)
22.5x - 135 + 22.5x + 135 = 9x^2 - 324
-> 9x^2 - 45x - 324 = 0 (solve for x)

Answer 18

where did the minus 45x come from?

Answer 19

22.5x + 22.5x = 45x

Answer 20

mmm if you were confused...?
" 22.5(x-6) + 22.5(x+6) = 9(x+6)(x-6) "
means 9(x+6)(x-6) - 22.5(x-6) - 22.5(x+6)
which I simplified to 9x^2 - 45x - 324

Answer 21

then factor out a 9
then factor... what do you get?