1. **State the problem:** A motor boat travels 24 km upstream and downstream. The speed of the boat in still water is 18 km/hr. The boat takes 1 hour more to go upstream than downstream. We need to find the speed of the current. 2. **Define variables:** Let the speed of the current be $x$ km/hr. 3. **Speeds upstream and downstream:** - Upstream speed = $18 - x$ km/hr - Downstream speed = $18 + x$ km/hr 4. **Time taken formula:** Time = Distance / Speed - Time upstream = $\frac{24}{18 - x}$ hours - Time downstream = $\frac{24}{18 + x}$ hours 5. **Given condition:** Time upstream is 1 hour more than time downstream $$\frac{24}{18 - x} = \frac{24}{18 + x} + 1$$ 6. **Solve the equation:** Multiply both sides by $(18 - x)(18 + x)$: $$24(18 + x) = 24(18 - x) + (18 - x)(18 + x)$$ Expand: $$432 + 24x = 432 - 24x + (18^2 - x^2)$$ $$432 + 24x = 432 - 24x + (324 - x^2)$$ Simplify: $$432 + 24x = 432 - 24x + 324 - x^2$$ $$432 + 24x = 756 - 24x - x^2$$ Bring all terms to one side: $$0 = 756 - 24x - x^2 - 432 - 24x$$ $$0 = 324 - 48x - x^2$$ Rewrite: $$x^2 + 48x - 324 = 0$$ 7. **Use quadratic formula:** $$x = \frac{-48 \pm \sqrt{48^2 - 4 \times 1 \times (-324)}}{2}$$ Calculate discriminant: $$48^2 = 2304$$ $$4 \times 324 = 1296$$ $$\sqrt{2304 + 1296} = \sqrt{3600} = 60$$ So, $$x = \frac{-48 \pm 60}{2}$$ Two solutions: - $$x = \frac{-48 + 60}{2} = \frac{12}{2} = 6$$ - $$x = \frac{-48 - 60}{2} = \frac{-108}{2} = -54$$ 8. **Interpretation:** Speed of current cannot be negative, so $$x = 6$$ km/hr. **Final answer:** The speed of the current is **6 km/hr**.