Complete question is;
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 hour
Step-by-step explanation:
The speed downstream will be given by; (v + u)
The speed when traveling back upstream is; (v - u)
We are told time it took to travel downstream = 1 hr
Let's denote time to travel upstream as t.
Now, distance = speed × time
Distance travelled downstream in an hour = (v - u)1
Distance it takes to get back to the raft is; (v - u)t
Thus;
(v + u)1 - (v - u)t = 6
(v + u) - (v - u)t = 6 - - - (eq 1)
Now, since the distance covered by the raft is 6 miles, it also did it in (1 + t) hours. Thus, the speed = u miles/hr
Thus, distance is;
u(1 + t) = 6 - - - (eq 2)
Putting u(1 + t) for 6 in eq 1,we have;
(v + u) - (v - u)t = u(1 + t)
v + u - vt + ut = u + ut
u and ut cancel out to give;
v - vt = 0
v = vt
t = v/v
t = 1 hour
