Finding Speed of Boat in Still Water and Current

Video Explanation

Question

A sailor goes 8 km downstream in 40 minutes and returns in 1 hour. Find the speed of the sailor in still water and the speed of the current.

Solution

Step 1: Let the Variables

Let speed of boat in still water = \(x\) km/h

Let speed of current = \(y\) km/h

Step 2: Convert Time

40 minutes = \(\frac{2}{3}\) hour

Step 3: Form the Equations

Downstream speed:

\[ \text{Speed} = x + y \]

\[ \frac{8}{2/3} = x + y \]

\[ x + y = 12 \quad (1) \]

— Upstream speed:

\[ \text{Speed} = x – y \]

\[ \frac{8}{1} = x – y \]

\[ x – y = 8 \quad (2) \]

Step 4: Solve by Elimination

Add equations (1) and (2):

\[ (x + y) + (x – y) = 12 + 8 \]

\[ 2x = 20 \]

\[ x = 10 \]

Step 5: Find the Value of y

Substitute in equation (1):

\[ 10 + y = 12 \]

\[ y = 2 \]

Conclusion

Speed of boat in still water:

\[ \boxed{10 \text{ km/h}} \]

Speed of current:

\[ \boxed{2 \text{ km/h}} \]