A river is flowing at a rate of 5 kmh A boat travels 12km up

A river is flowing at a rate of 5 km/h. A boat travels 12km upstream and 36km downstream in a total of 9hours. What is the speed of the boat in still water?

Solution

We know that the ratio of the distance travel is 3:1 36:12
We then make the distance equal by dividing the distance traveled downstream by 3
We know the speed of the river=5 km/h
x=time it takes to travel upstream
9-x time it takes to travel downstream
5x=1/3(9-x)(5)
This equation is based on D=(rate)(time)
Muliply both sides by 3
15x=(9-x)(5)
Use the distributive property
15x=45-5x
add 5x to both sides
20x=45
divide both sides by 20 x=2.25 9-x=6.75
Lets check the ratio to make sure that it is 3:1
6.75/2.25=3
Let\'s plug into the D=TR to calculate rate
36/6.75=5.33 km/hr
12/2.25=5.33 km/hr
The rate is the same.