Question

A boat traveled 96 miles downstream and back. The trip downstream took 4 hours. The trip back took 12 hours. Find the speed of the boat in still water and the speed of the current

Answer 1

Answer:

Speed of boat is still water: 16 miles per hour.

Speed of current: 8 miles per hour.

Step-by-step explanation:

Let x represent speed of boat in still water and y represent speed of current.

Downstream speed would be $x+y$.

Upstream speed would be $x-y$.

We have been given that a boat traveled 96 miles downstream and back. The trip downstream took 4 hours.  

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

$x+y=\frac{96}{4}...(1)$

$x+y=24...(1)$

We are also told that the trip back took 12 hours. We can represent this information in an equation as:

$x-y=\frac{96}{12}...(2)$

$x-y=8...(2)$

Upon adding equation (1) and equation (2), we will get:

$x+x+y-y=24+8$

$2x=32$

$\frac{2x}{2}=\frac{32}{2}$

$x=16$

Therefore, the speed of boat in the still water is 16 miles per hour.

Upon substituting $x=16$ in equation (1), we will get:

$16+y=24$

$16-16+y=24-16$

$y=8$

Therefore, the speed of the current is 8 miles per hour.