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:

$d=r \times t$

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

So, $t=\frac{d}{r}$

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 = $\frac{14}{u+6}$ 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 = $\frac{2}{u-6}$ hr

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

So, $\frac{14}{u+6}=\frac{2}{u-6}$

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 = $\frac{14}{u+6}$

= $\frac{14}{8+6}$

= 1 hr

Now, Time taken in going upstream = $\frac{2}{u-6}$

= $\frac{2}{8-6}$

= 1 hr

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