Question

A motor boat and a raft start traveling downstream. After 1 hour, the boat turns around and travels back until it reaches the raft. If the distance traveled by the raft is 6 miles, what is the speed of the current?

Answer 1

Speed of the current is 3 miles per hour.

Explanation:

Raft and a motor boat starts traveling downstream at the same time from point B towards point A downstream.

Let the speed of the motorboat = v miles per hour

and speed of the current = u miles per hour

Motorboat travels downstream with the speed = (v + u) miles per hour

Distance traveled by motorboat in 1 hour (Distance AC) = (v + u)×1 miles

Now motorboat turns around and reaches point B where it meats the raft against the river stream.

Speed of motorboat against the current = (v - u) miles per hour

Let it takes to reach at point B = t hours

Distance covered AB = (v - u)t miles

From the figure attached,

Distance BC = AC - AB

6 = (v + u) - (v - u)t ------(1)

Now raft covered the distance 6 miles in (1 + t) hours with the speed = u miles per hour.

Equation will be u(t + 1) = 6 --------(2)

Now by equating both the equations

(v + u) - (v - u)t = u(t + 1)

v + u - vt + ut = ut + u

v - vt = 0

vt = v

t = 1 hours

From equation (2)

u(1 + 1) = 6

2u = 6

u = 3 miles per hour.

Therefore, speed of the current will be 3 miles per hour.