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. a What amount of time does it take the boat to reach the raft after it turns around?

Answer 1

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