Question

A speedboat drives 3 times the speed of the current. Thus, it travels downriver for 700 miles 3 hours more than it takes to travel upriver for 325 miles. How do you find the speed of the boat in still water?

Answer 1

Speed of boat (in still water)`= 12.5 (" miles")/(" hour")`

Explanation:

Define:
`color(white)("XXX")b`: speed of boat in still water
`color(white)("XXX")c`: speed of current
`color(white)("XXX")s_(down)`: speed of boat going downstream
`color(white)("XXX")s_(up)`: speed of boat going upstream
`color(white)("XXX")t_(down)`: time to go 700 miles downstream
`color(white)("XXX")t_(up)`: time to go 325 miles upstream

`b = 3c` (given)

`s_(down) = 4c` (speed of boat plus speed of current)
`s_(up) = 2c` (speed of boat minus speed of water)

`t_(down) = 700/(s_(down)) = 700/(4c)`
`t_(up) = 325/(s_(up)) = 325/(2c)`

`t_(down) = t_(up) +3` (given)

`700/(4c)=325/(2c)+3`

`rarr 700/4 = 325/2 +3c`

`rarr 3c = 700/4 - 325/2 = 700/4-650/4 = 50/4 = 12.5`

(and remember that the speed of the boat in still water is `3c`)