To solve this problem, we need to understand the relationship between speed, distance, and time.

Key Formulas:

• Speed = $\frac{\text{Distance}}{\text{Time}}$
• Time = $\frac{\text{Distance}}{\text{Speed}}$

Given:

• Let the initial speed of the car be $S$ and the time taken initially be $T$.
• The new speed after a 50% increase is $1.5S$.

To Find:

• The reduction in time.

Calculation:

• The original time taken $T = \frac{D}{S}$, where $D$ is the distance.
• The new time taken $T' = \frac{D}{1.5S}$.

Now, find the ratio of the new time $T'$ to the original time $T$: $\frac{T'}{T} = \frac{\frac{D}{1.5S}}{\frac{D}{S}} = \frac{S}{1.5S} = \frac{1}{1.5} = \frac{2}{3}$ This means the new time $T'$ is $\frac{2}{3}$ of the original time $T$.

Reduction in Time:

• The reduction in time $T - T' = T - \frac{2}{3}T = \frac{1}{3}T$.

Thus, the time taken is reduced by 33.33%.

Would you like more details or have any questions?

Further Questions:

1. What happens to the time if the speed is doubled instead of increased by 50%?
2. How would the time change if the speed is decreased by 25%?
3. What is the relationship between time and speed if the distance remains constant?
4. How does the distance affect time if the speed is constant?
5. If the car was traveling at 60 km/h, how long would it take to cover 120 km?

Tip:

Remember, when speed increases, the time taken decreases proportionally if the distance remains constant.