Question

Two friends went rowing on the river. They first traveled with current for 3 hours. The way back took them 4 hours and 48 minutes. Find the speed of the river's current if they can row in still water at a speed of 6.5 mph.

Answer 1

The speed of the current is 1.5 mph.

Explanation:

We need to use an expression to each movement. For the first one, we know that the boat is traveling with the current, this means that the boat and current speed sum, because they have the same direction. On the other hand, in the second movement, the speeds subtract because the boat is moving agains the direction of the current.

Now, we now that the speed of the boat is 6.5 mph, and the speed of the current is unknown, we'll call it c. Also, we assume that it's a constant movement, in that case we can apply:
`d = vt`; where d is distance, v is speed and t is time.

First movement:

`d_(1) = (6.5 + c)(3hr)`

Second movement:

`d_(2) = (6.5 - c)(4.8hr)`

4.8 is the converted, because the problem gives 4 hours and 48 minutes, and we have to transform those minutes into hours. We know that 1hr equals 60 min:

`48min(1hr)/(60min)=0.8hr`; so, the time for the second movement is 4.8hr.

Now, the problem say that the boat went back, this means that both movements have the same distance covered, so we can equalize both equations, then isolate c and find the speed of the current:

`d_(1)=d_(2) \\(6.5 + c)(3hr)=(6.5 - c)(4.8hr)\\19.5 + 3c = 31.2-4.8c\\4.8c + 3c=31.2-19.5\\7.8c=11.7\\c=(11.7)/(7.8)=1.5mph`

Therefore, the speed of the current is 1.5 mph.

Answer 2

1.5 mph

Explanation:

Let speed of boat be x

let speed of current be c

Also, note D = RT

D is distance

R is rate

T is time

Now, for first leg, we can write:

(x+c)3 = D

And for second leg , we can write:

(x-c)4.8 = D [note 4 hour 48 minutes is 4.8 hours]

We can equate both D's to get:

(x+c)3 = (x-c)4.8

3x + 3c = 4.8x - 4.8c

7.8c = 1.8x

We know x = 6.5 [given], plugging it in and solving for c:

7.8c = 1.8(6.5)

c = 1.5

Speed of Current = 1.5 miles per hour