Question

a motorboat takes 3 hours to travel 108 kilometers going upstream. the return trip takes 2 hours going downstream. what is the rate of the boat in still water and what is the rate of the current? rate of the boat in still water: \\(\square \frac{\text{km}}{\text{h}}\\) rate of the current: \\(\square \frac{\text{km}}{\text{h}}\\)

Explanation:

Step1: Find upstream and downstream rates

Upstream rate: Distance ÷ Time = \( \frac{108}{3} = 36 \) km/h.
Downstream rate: \( \frac{108}{2} = 54 \) km/h.

Step2: Solve for boat and current rates

Let \( b \) = boat rate, \( c \) = current rate.
Upstream: \( b - c = 36 \)
Downstream: \( b + c = 54 \)

Add equations: \( 2b = 90 \) → \( b = 45 \) km/h.
Substitute \( b \) into \( b - c = 36 \): \( 45 - c = 36 \) → \( c = 9 \) km/h.

Answer:

Rate of the boat in still water: \( \boldsymbol{45} \) \( \frac{\text{km}}{\text{h}} \)
Rate of the current: \( \boldsymbol{9} \) \( \frac{\text{km}}{\text{h}} \)