Question

a tourist boat is used for sightseeing in a nearby river. The boat travels 2.4 miles downstream and in the same amount of time. it travels 1.8 miles upstream, if the boat travels at an average speed of 21 miles per hour in the still water, find the current of the river. show me the work

Answer 1

The current of the river has a speed of 3 miles per hour

Explanation:

Let's call v the speed of the boat in calm waters.

We know that:

`v = (d)/(t)`

Where d is the distance in miles and t is the time

When the boat travels down we have to:

`d=2.4\ miles`

If s is the speed at which the boat travels downstream and c is the speed of the river then

`s=(v+c)`

And

`t=(d)/(s)\\\\t=(d)/(v+c)\\\\t=(2.4)/(21+c)`

When the boat travels upstream we have to:

`d=1.8\ miles`

`s=(v-c)`

`t=(d)/(s)\\\\t=(d)/(v-c)\\\\t=(1.8)/(21-c)`

We know that the time he navigate upstream is the same time he navigate downstream

Then:

`(2.4)/(21+c)=(1.8)/(21-c)`

We solve the equation for c

`2.4*(21-c)=(21+c)*1.8`

`50.4-2.4c=37.8+1.8c`

`50.4-37.8=1.8c+2.4c`

`4.2c=12.6`

`c=(12.6)/(4.2)`

`c=3\ miles\ per\ hour`