Question

A boat on a river travels downstream between two points, 20 mi apart, in one hour. The return trip against the current takes 2 1/ 2 hours (2hours and a half). What is the boat's speed (in still water)?b) How fast does the current in the river flow?

Answer 1

Answer:

The speed of boat in still water is 14 miles per hour.

The speed of current is 6 miles per hour.

Step-by-step explanation:

Let v represent the speed of boat in still water and c represent speed of current.

We have been given that a boat on a river travels downstream between two points, 20 miles apart, in one hour.

The speed of boat downstream would speed of boat in still water plus speed of current that is $(v+c)$.

The return trip against the current takes 2 1/ 2 hours. The speed of boat against current would speed of boat in still water minus speed of current that is $(v-c)$.

$\text{Speed}=\frac{\text{Distance}}{\text{Time}}$

Substituting our given values, we will get:

$v+c=\frac{20}{1}...(1)$

$v-c=\frac{20}{2.5}...(2)$

Adding both equations, we will get:

$v+c+(v-c)=\frac{20}{1}+\frac{20}{2.5}$

$v+c+v-c=\frac{20}{1}+\frac{20}{2.5}$

$2v=20+8$

$2v=28$

$\frac{2v}{2}=\frac{28}{2}$

$v=14$

Therefore, the speed of boat in still water is 14 miles per hour.

To find the speed of the current in the river, we will substitute $v=14$ in equation (1) as:

$14+c=\frac{20}{1}$

$14+c=20$

$14-14+c=20-14$

$c=6$

Therefore, the speed of current is 6 miles per hour.