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.