The excursion boat on the river takes 2 hours to make the trip to a point 12 miles upstream and to return. If the rate at which the boat travels in still water is 5 times the rate of the river current, what is the rate of the current?

  2.5 miles per hour

Step-by-step explanation:

Let c represent the rate of the current. Then the rate of the boat in still water is 5c. The current subtracts from this rate going upstream, and adds going downstream.

The relation between time, speed, and distance is ...

  time = distance/speed

The sum of times upstream and downstream is 2 hours, so we have ...

  12/(5c -c) +12/(5c +c) = 2

  3/c +2/c = 2 . . . . . simplify

  5 = 2c . . . . . . . . . . multiply by c

  c = 5/2 = 2.5 . . . . miles per hour

The rate of the current is 2.5 miles per hour.

the rate of the current is 2.5 mph.

Step-by-step explanation:

Let x represent the rate of the current.

If the rate at which the boat travels in still water is 5 times the rate of the river current, it means that the rate of the boat travels in still water is 5x mph.

Time = distance/time

Assuming the boat travels against the current while going upstream. Its total speed would be

5x - x = 4x mph

Time spent in travelling 12 miles upstream is

12/4x

Assuming the boat travels with the current while going downstream, Its total speed would be

5x + x = 6x mph

Time spent in travelling 12 miles upstream is

12/6x

Since the total time spent is 2 hours, it means that

12/4x + 12/6x = 2

3/x + 2/x = 2

Multiplying both sides by x, it becomes

3 + 2 = 2x

2x = 5

x = 5/2

x = 2.5 mph

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