Question

Please help me?!!

a motorboat takes 5 hours to travel 150 Miles going Upstream. the return trip takes 3 hours going Downstream .what is the rate of the boat in still water and what is the rate of the current ?​

Answer 1

The the rate of the motorboat in still water is 40 km/h; the rate of the current is 10 km/h.

Explanation:

Let u be the rate of the motorboat in still water (in kilometers per hour),

let v be the rate of the current.

Then the rate of the motorboat going downstream is u+v km/h,

while its rate going upstream is u-v km/h.

From the other side, the rate of the motorboat going downstream is 150/3=50km/h = 30 km/h.

Thus you have these two equations

u + v = 50 (1) (for the rate downstream), and

u - v = 30 (2) (for the rate upstream).

To solve the system, add equations (1) and (2). You will get

2u = 50 + 30 = 80; hence,

u = 80/2 = 40 km/h.

Then from the equation (1), v = 50 - u = 50 - 40 = 10 km/h.

ANSWER. The the rate of the motorboat in still water is 40 km/h; the rate of the current is 10 km/h.