Question

It takes a boat going upstream 5 hours to cover the same distance, as it would cover in 3 hours going downstream. What is the speed of the boat if the speed of the current is 2 kilometers per hour?

Answer 1

Answer:

The speed of the boat is 8 km/h.

Step-by-step explanation:

Assuming that the boat's speed is "x" without the influence of the current, then when it's going upstream it's speed is "x - 2" and when it's going downstream it's speed is "x + 2". Assuming that the distance is "y", we can then apply the formula for average speed in both cases to create a system of equations as shown below:

speed = distance / time

Upstream:

x - 2 = y / 5

5*x - 10 = y

5*x -y = 10

Downstream:

x+2 = y / 3

3*x + 6 = y

3*x - y = -6

System:

5*x -y = 10

3*x - y = -6

Multiplying the second equation by -1:

5*x - y = 10

-3*x + y = 6

Adding both equations:

2*x = 16

x = 16/2 = 8 km/h

The speed of the boat is 8 km/h.