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 his trip in a total of 9hours. 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 operators needs? (this is an explanation kind of answer)

The boat must go on the lake at the speed of 9 mph.  

Step-by-step explanation:

t 1 + t 2 = 9

d = ( v - 6 ) * t 1 ( against the current )

d = ( v + 6 ) * t 2 ( back )

t 1 = 9 - t 2

22.5 = ( v - 6 ) * ( 9 - t 2 )

22.5 = ( v + 6 ) * t 2

76.5 = 9 v - v t 2 + 6 t 2

+

22.5 =   v t 2 + 6 t 2

99 = 9 v + 12 t 2

9 v = - 12 t 2 + 99  / : 99

v = - 4/3 t 2 + 11

22.5 = ( - 4/3 t 2 + 11 ) + t 2 + 6 t 2

4 t 2²  - 51 t 2 + 67.5 = 0

t 2 = (51+/- √(2601 - 1080)) /8 = ( 51 - 39 ) /8 = 1.5

v = -4/3 * 1.5 + 11 = - 2 + 11 = 9 mph

idk

step-by-step explanation: