Question

A rowing team rowed an average of 15.2 miles per hour with the current and 8.4 miles per hour against the current. Determine the​ team's rowing speed in still water and the speed of the current.

Answer 1

Answer:

Team's rowing speed in still water: 11.8 miles per hour.

Speed of the current: 3.4 miles per hour.

Step-by-step explanation:

Let r represent team's rowing speed in still water and speed of current be c.

Rowing speed with current would be $r+c$ and rowing speed against current would be $r-c$.

We have been given that a rowing team rowed an average of 15.2 miles per hour with the current. We can represent this information in an equation as:

$r+c=15.2...(1)$

We are also told that rowing team rowed an average of 8.4 miles per hour against the current. We can represent this information in an equation as:

$r-c=8.4...(2)$

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

$r+r+c+(-c)=15.2+8.4$

$r+r+c-c=15.2+8.4$

$2r=23.6$

$\frac{2r}{2}=\frac{23.6}{2}$

$r=11.8$

Therefore, teams's rowing speed in still water was 11.8 miles per hour.

Upon substituting $r=11.8$ in equation (1), we will get:

$11.8+c=15.2$

$11.8-11.8+c=15.2-11.8$

$c=3.4$

Therefore, speed of the current was 3.4 miles per hour.