Question

Question 27 a motorboat takes 3 hours to travel 144km going upstream. the return trip takes 2 hours going downstream. what is the rate of the boat in still water and what is the rate of the current

Answer 1

In this item, we let x be the rate of the boat in still water and y be the rate of the current.

Upstream. When the boat is going upstream, the speed in still water is deducted by the speed of the current because the boat goes against the water. The distance covered is calculated by multiplying the number of hours and the speed.
                 (x - y)(3) = 144

Downstream. The speed of the boat going downstream is equal to x + y because the boat goes with the current.
                (x + y)(2) = 144

The system of linear equations we can use to solve for x is,
                  3x - 3y  = 144
                  2x + 2y = 144

We use either elimination or substitution.
 
We solve for the y of the first equation in terms of x,
                   y =  -(144 - 3x)/3

Substitute this to the second equation,
            2x + 2(-1)(144 - 3x)/3 = 144
The value of x from the equation is 60

ANSWER: 60 km/h