Question

A cabin cruiser traveling with the current went 12 mi in 1 h. Traveling against the current, it took 2 h to go the same distance. Find the rate of the cabin cruiser in calm water and the rate of the current

Answer 1

The rate of the cabin cruiser in calm water is 9 mph and the rate of the current 3 mph

Explanation:

Given:

Speed of cabin cruiser travelling with then current = 12 mi in 1 h.

Against the current, it took 2 h to travel the same distance.

To Find:

The rate of the boat in calm water and the rate of the current = ?

Solution:

Let boat speed in calm water be s

Let rate of the current be c

Then

(s-c) = effective speed upstream

and

(s+c) = effective speed downstream

Writing a distance equation for each trip:

distance =
`time * \text{effective speed}`

1(s + c) = 12

2(s - c) = 12

On the first equation divide both sides by 1

On the second equation divide both sides by 2

s + c = 12

s - c = 6

Now addition of the above two equations gives

2s = 18

s = 9 mph, boat speed in calm water

Lets substitute s value to find c value

s + c = 12

9 + c = 12

c = 12 - 9

c = 3 mph is the current