Question

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Answer 1

Answer:

$6\text{ mph}$

Step-by-step explanation:

To find the the distance between A and B, use $d=rt$, where $d$ is distance, $r$ is rate/speed, and $t$ is time.

The raft travels from A to B in 6 hours at a rate of 3 mph. Thus, the distance from A to B must be:

$d=3\cdot 6=18$ miles.

Since the motorboat travels the same distance in 2 hours, its rate/speed must be:

$18=2r,\\r=\frac{18}{2}=9\text{ mph}$

Because the raft is drifting, the speed of the current must be $3\text{ mph}$ in the direction of the raft (from A to B). Thus, let the motorboat's speed be $m$:

$m+3=9,\\n=\boxed{6\text{ mph}}$

Answer 2

Answer:

Time taken by the un powered raft to cover this distance is T = 192.12 hr

Step-by-step explanation:

Let speed of boat = u

Speed of current = v

Let distance between A & B = 100 km

Time taken in downstream = 32 hours

u + v = 3.125 ------ (1)

Time taken in upstream = 48 hours

u - v = 2.084 ------- (2)

By solving equation (1) & (2)

u = 2.6045

v = 0.5205

Now the time taken by the un powered raft to cover this distance

Because un powered raft travel with the speed of the current.

T = 192.12 hr

Therefore the  time taken by the un powered raft to cover this distance is

T = 192.12 hr