Question

If a person rows to his favorite fishing spot 14 miles downstream in the same amount of time that he rows 2 miles upstream and if the current is 6 ​mph, find how long it takes him to cover 16 miles.

It will take the person _ ​hour(s) to cover a distance of 16 miles.

Answer 1

We will use distance formula which states:

`d=r * t`

where 'd' is the distance, 'r' is rate or speed and 't' is time taken.

So,
`t=(d)/(r)`

Let 'u' be the speed of boat in still water.

A person rows 14 miles downstream to the fishing spot.

So, the speed of boat downstream = (u+6) mph

Time taken by boat to go downstream =
`(14)/(u+6)` hr

He rows 2 miles upstream from the fishing spot.

So, the speed of boat upstream = (u-6) mph

Time taken by boat to go upstream =
`(2)/(u-6)` hr

Since, The person took same amount of time in going downstream and then going upstream.

So,
`(14)/(u+6)=(2)/(u-6)`

Cross multiplying, we get

`14 (u-6)= 2(u+6)`

`14u - 84 = 2u + 12`

`12u = 96`

u = 8

So, speed of boat in still water is 8mph.

Now, Time taken in going downstream =
`(14)/(u+6)`

=
`(14)/(8+6)`

= 1 hr

Now, Time taken in going upstream =
`(2)/(u-6)`

=
`(2)/(8-6)`

= 1 hr

So, total time taken to cover 16 miles is 2 hours.