Question

Use the three steps to solve the problem.

The excursion boat on the river takes 2½ 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?

Answer 1

Try this option (see the attacthed file; answer is marked with red colour); note, that

`t_(c-) = upstream \ time; \ t_(c+)=downstream \ time.`

answer: 2 m/h.

Answer 2

Let x be the speed of current ( miles per hour ),

Thus, as per statement,

The speed of boat in still water = 5x miles per hour,

⇒ The speed in upstream = 5x - x = 4x miles per hour,

And, the speed in downstream = 5x + x = 6x miles per hour,

We know that,

`Time = (Distance)/(Time)`

Given distance = 12 miles,

So, the time taken in upstream =
`(12)/(4x)=(3)/(x)\text{ hour}`

And, the time taken in downstream =
`(12)/(6x)=(2)/(x)\text{ hours}`

Total time taken = 2½ hours

`\implies (3)/(x)+(2)/(x)=2(1)/(2)`

`\implies (5)/(x)=(5)/(2)`

`\implies x = 2`

Hence, the speed of current is 2 miles per hour.