Question

The velocity of a boat is 18 km/h in still water. It takes one hour more to travel 24 km in downstream and 24 km in upstream. Find the speed of the current.

Hint:

In boat-stream problems, remember: Downstream speed = (Boat speed + Current speed), Upstream speed = (Boat speed – Current speed).

Answer 1

Step 1: Let the speed of the current be $x$ km/h.
Then, Downstream speed = $(18 + x)$ km/h, Upstream speed = $(18 - x)$ km/h.

Step 2: Use the time formula.
\[ \text{Time} = \dfrac{\text{Distance}}{\text{Speed}} \] Given that the time for upstream journey is one hour more than that for downstream: \[ \dfrac{24}{18 - x} = \dfrac{24}{18 + x} + 1 \]
Step 3: Simplify the equation.
\[ \dfrac{24}{18 - x} - \dfrac{24}{18 + x} = 1 \] \[ 24 \left( \dfrac{(18 + x) - (18 - x)}{(18)^2 - x^2} \right) = 1 \Rightarrow 24 \left( \dfrac{2x}{324 - x^2} \right) = 1 \Rightarrow 48x = 324 - x^2 \Rightarrow x^2 + 48x - 324 = 0 \]
Step 4: Solve for $x$.
\[ x^2 + 48x - 324 = 0 \Rightarrow x = 6 \, \text{(taking positive value since speed cannot be negative)} \] Step 5: Conclusion.
Hence, the speed of the current is 6 km/h.