1. ## distance-speed problem

Water in the murray flows at 4km/hr. If a boat takes 3 hours to complete 32km round trip (16 km downstream and 16km back upstream), what is the boat's relative speed to the water?
so far i have found that when going upstream, the equation is (x + 4) and when going dfownstream the equation is (x-4) x being the speed of the boat. and the boats speed is 32/3
but i am unsure how to turn this into an algebratic equation.

Zac

2. Hello, Zac!

You know: .$\displaystyle \text{Distance} \:=\:\text{Speed} \times \text{Time} \quad\Rightarrow\quad T \:=\:\frac{D}{S}$

Water in the murray flows at 4 km/hr.
If a boat takes 3 hours to complete 32 km round trip,
what is the boat's relative speed to the water?

so far i have found that when going upstream, the equation is (x + 4)
and when going downstream the equation is (x - 4) . . . . These are reversed

Let $\displaystyle x$ = boat's speed.

Going upstream, its speed is smaller: .$\displaystyle x-4$
Going downstream, its speed is greater: .$\displaystyle x + 4$

It went upstream $\displaystyle 16$ km at $\displaystyle x-4$ km/hr.
. . This took: .$\displaystyle \frac{16}{x-4}$ hours.

It went downstream $\displaystyle 16$ km at $\displaystyle x+4$ km/hr.
. . This took: .$\displaystyle \frac{16}{x+4}$ hours.

The total trip took 3 hours: . $\displaystyle \frac{16}{x-4} + \frac{16}{x+4} \:=\:3\quad\hdots There!$