1. ## Word Problem Help

I need help with this stupid word problem. I'm at my girlfriend house and I left my book at home.

A stream flows at a rate of 4 mph. A boat travels 70 miles downstream and returns in a total time of 6 hrs. What is the speed of the boat in still water.

I am a complete retard when it comes to word problems. Can someone at least point out how I can get the correct formula for this?

2. Hi, I do not know if this is correct or not but this is going to be my best guess.

The boat travels for 6 hours and the stream flows at 4 mph.

In total that would be 24 MPH?

70-24=46 Mph

Not sure if it's correct as I said above but I think it should be.

EDIT: mine is completely wrong didn't see that it said STILL water.

3. Hello, BuhRock!

A stream flows at a rate of 4 mph.
A boat travels 70 miles downstream and returns in a total time of 6 hrs.
What is the speed of the boat in still water?

We know that: .$\displaystyle \text{(Distance)} \:=\:\text{(Speed)} \times \text{(Time)} \quad\Rightarrow\quad T \:=\:\dfrac{D}{S}$

Let $\displaystyle \,b$ = speed of the boat in still water.

Going downsream (with the current), the boat's speed is: .$\displaystyle b + 4$ mph.
To go 70 miles downsteam, it takes: $\displaystyle \dfrac{70}{b+4}$ hours.

Going upstream (against the current), the boat's speed is: .$\displaystyle b - 4$ mph.
To go 70 miles upstream, it takes: $\displaystyle \dfrac{70}{b-4}$ hours.

The total time is six hours.
There is our equation! . . . . . $\displaystyle \dfrac{70}{b+4} + \dfrac{70}{b-4} \:=\:6$

Multiply by $\displaystyle (b+4)(b-4)\!:\;\;70(b-4) + 70(b+4) \:=\:6(b+4)(b-4)$

. . which simplifies to: . $\displaystyle 3b^2 - 70b - 48 \:=\:0$

. . which factors: . $\displaystyle (b-24)(3b + 2) \:=\:0$

. . and has roots: . $\displaystyle b \:=\:24,\:-\frac{2}{3}$

The boat's speed in still water is: .$\displaystyle 24\text{ mph.}$