## A motor boat can travel 45 km downstream in 2 hr 30 mins

Quadratic equations and inequalities, variation equations, function notation, systems of equations, etc.
little_dragon
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### A motor boat can travel 45 km downstream in 2 hr 30 mins

A motor boat can travel 45 km downstream in 2 hr and 30 min, and 39 km upstream in 3 h and 15 min. What is the speed of the boat in still water? What is the speed of the current?

I know there's a trick to this, but I can't remember what it is?

stapel_eliz
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You're right about the "trick": you have to keep in mind that "upstream" and "downstream" (just like "with the wind" and "against the wind") indicate competing or cooperating powers.

Suppose you turn the engine off in the motor boat. The boat would still move, right? It would go downstream, because the current is pushing it. Even though the speedometer reads "zero", the boat would still be in motion. If you turn the engine back on and head downstream, that pushing would still be happening; you would add the speed of the current to the speedometer reading. If you headed upstream, you would subtract the speed of the current from the speedometer, because the current would be pushing against the boat's progress.

Have fun!

Eliz.

Karl
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### Re: A motor boat can travel 45 km downstream in 2 hr 30 mins

Let me add a little more to Ms. Stapel's response, hopefully without giving too much away. The problem asks for two things -- that is there are two questions at the end of it. Both are velocities; that is the velocity of the boat in still water, v, and the velocity of the current, w.

Upstream the boat's velocity is v-w. Downstream the boat's velocity is v+w.

Remember the velocity equation: distance traveled is equal to velocity times time.

The problem gives you two such equations. One is distance = 45 km and time = 2.5 hours. Downstream the boat goes v+w.

I'll let you extract the parameters for the second (upstream) equation yourself.

In the end you will have two equations in two unknowns, v and w. Solve them simultaneously in the usual way.

little_dragon
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Upstream the boat's velocity is v-w. Downstream the boat's velocity is v+w.
I remembered "d=rt", but I always forget the adding and subtracting. Thanks!!!