Question

The speed of a stream is 3 mph. A boat travels 4 miles upstream in the same time it takes to travel 10 miles downstream. What is the speed of the boat in still​ water?

Answer 1

this is a motion problem that usually involves `d=r*t` and this formula is interchangeable for whatever variable we seek.

Explanation:

When we do these type of problems it is very handy for us to create a small chart of our variables and what we have access to.

The slower boat is the one going upstream let us call it `S` for slower.

The faster boat is `F` for faster

we do not know the speed of the boat let us call that `r` for the unknown rate

`F` `10/(r+3)` because it is going downstream naturally the speed of the stream further accelerates our little boat.

`S` `4/(r-3)` because the boat is travelling against the stream the boat is slowed down.

we can equalize them to find the speed of the boat without the other factors bothering us now :)

`10/(r+3) = 4/(r-3)` from here you can cross multiply

`10(r-3) = 4(r+3)`

now we distribute...

`10r-30 = 4r + 12`

move our variable to one side to isolate it further.

`10r -4r = 30 + 12`

`6r = 42`

we divide by a form of one to isolate the variable further (remember to apply to both sides)

`(6r)/6 = 42/6`

`r = 7` the boat in still water is 7 miles per hour