Subjects algebra

Vehicle Speeds 457554

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Vehicle Speeds 457554


1. **State the problem:** A car travels 11 kph faster than a bus. The car covers 152 km in the same time the bus covers 110 km. We need to find the speed of each vehicle. 2. **Define variables:** Let the speed of the bus be $x$ kph. 3. **Express the car's speed:** The car's speed is $x + 11$ kph. 4. **Use the formula for time:** Time = Distance / Speed. 5. **Set up the equation:** Since the times are equal, $$\frac{152}{x+11} = \frac{110}{x}$$ 6. **Solve the equation:** Cross-multiply: $$152x = 110(x + 11)$$ 7. **Expand and simplify:** $$152x = 110x + 1210$$ 8. **Bring terms to one side:** $$152x - 110x = 1210$$ $$42x = 1210$$ 9. **Solve for $x$:** $$x = \frac{1210}{42} = 28.81$$ (approx) 10. **Find the car's speed:** $$x + 11 = 28.81 + 11 = 39.81$$ kph (approx) **Answer:** The bus travels at approximately 28.81 kph, and the car travels at approximately 39.81 kph.