1. ## Velocity

I can't solve this exercise, it's intended for ~13 year olds, so you can't use rational equations.
Here it is: A motor boat swam 45 km in the river in 3 hours, and back in 5 hours.
a) what is the speed of the river flow?
b) what is the speed of the motor boat?

2. Originally Posted by Evaldas
I can't solve this exercise, it's intended for ~13 year olds, so you can't use rational equations.
Here it is: A motor boat swam 45 km in the river in 3 hours, and back in 5 hours.
a) what is the speed of the river flow?
b) what is the speed of the motor boat?
Not sure if you are looking for such a reasoning:

1. The boat is going down the river at a speed of $\displaystyle \dfrac{45\ km}{3\ h} = 15\ \dfrac{km}h$
and it is going up the river at a speed of $\displaystyle \dfrac{45\ km}{5\ h} = 9\ \dfrac{km}h$

2. In the first case the speed of the flowing water is added to the speed of the boat through the water and in the second case the speed of the flowing water is subtracted from the speed of the boat through the water. Therefore the mean of both velocities must be the speed of the boat through the water:

$\displaystyle speed_{boat} = \dfrac{15\ \frac{km}h + 9\ \frac{km}h}2=12\ \frac{km}h$

then the speed of the flowing water must be $\displaystyle speed_{water}=3\ \frac{km}h$

3. Yes! Those are the right answers. Thank you!

4. Hello, Evaldas!

This exercise is intended for ~13 year olds, so you can't use rational equations.

A motorboat went 45 km in the river in 3 hours, and back in 5 hours.
. . (a) What is the speed of the river flow?
. . (b) What is the speed of the motorboat?

The boat went 45 km down the river (with the current) in 3 hours.
. . Its speed was: .$\displaystyle \frac{45}{3} \:=\:15$ km/hr.

The boat went 45 kmn up the river (against the curent) in 5 hours.
. . Its speed was: .$\displaystyle \frac{45}{5} \:=\:9$ km/hr.

The actual speed of the boat is the average of these two speeds:

. . Speed of motorboat: .$\displaystyle \dfrac{15 + 9}{2} \:=\:\dfrac{24}{2} \:=\:12\text{ km/hr.}$

Then the speed of the river flow is: .$\displaystyle 3\text{ km/hr.}$