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Answer:
Speed of the current is 3 miles per hour.
Step-by-step 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.
