Question

A motorboat is able to travel at a speed of 20km/hr in still water. In 8 hours, the boat traveled 20km against the current and 180km with the current. Find the speed of the current

Answer 1

10 km/hr.

Explanation:

Speed of the boat with the current = 20 + c where c is the speed of the current.

Against the current the speed is 20 - c.

Distance = speed * time :

With the current:

180 = (20 + c)t..........A

Against the current:

20 = (20 - c)(8- t)......B

Solving this system of equations:

From A:

t = 180/(20 + c)

So

20 = (20 - c)(8 - 180/(20+c))

160 - 3600/(20 + c) - 8c + 180c/(20 + c) = 20

Mltiplying throagh by (20 + c):

160(20 + c) - 3600 - 8c(20 + c) + 180c = 20(20 + c)

3200 + 160c - 3600 - 160c - 8c^2 + 180c - 400 - 20c = 0

-8c^2 + 160c - 800 = 0

8c^2 - 160c + 800 = 0

c^2 - 20c + 100 = 0

(c - 10)*2 = 0

c = 10

So the speed of the crrent = 10 km/hr