To find the percentage decrease in speed, we first need to understand the relationship between speed, distance, and time. Speed is calculated as:

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

Let's denote:

• $D$ as the distance from the person's home to their office.
• $S_1$ as the normal speed.
• $S_2$ as the speed today.
• $T_1 = 45$ minutes as the normal time.
• $T_2 = 60$ minutes as the time today.

Step 1: Express the Speeds in Terms of Distance and Time

The normal speed, $S_1$, is:

$S_1 = \frac{D}{T_1} = \frac{D}{45}$

The speed today, $S_2$, is:

$S_2 = \frac{D}{T_2} = \frac{D}{60}$

Step 2: Find the Percentage Decrease in Speed

The percentage decrease in speed can be calculated using the formula:

$\text{Percentage Decrease} = \left( \frac{S_1 - S_2}{S_1} \right) \times 100$

Substitute the expressions for $S_1$ and $S_2$:

$\text{Percentage Decrease} = \left( \frac{\frac{D}{45} - \frac{D}{60}}{\frac{D}{45}} \right) \times 100$

Simplify the expression:

$\text{Percentage Decrease} = \left( \frac{\frac{60D - 45D}{2700}}{\frac{D}{45}} \right) \times 100$

$\text{Percentage Decrease} = \left( \frac{15D}{2700} \times \frac{45}{D} \right) \times 100$

$\text{Percentage Decrease} = \left( \frac{15 \times 45}{2700} \right) \times 100$

Calculate the value:

$\text{Percentage Decrease} = \left( \frac{675}{2700} \right) \times 100 = 25$

Conclusion

The person's speed decreased by 25% today as compared to their normal speed.

Would you like more details or have any questions?

Here are 5 related questions that could deepen your understanding:

1. How would the percentage decrease change if the time taken today was 75 minutes instead?
2. If the person's speed increased by 25% instead, how long would the journey take?
3. What is the effect on speed if the distance doubles but time remains the same?
4. How do you calculate average speed if the journey time varies over different days?
5. If the time decreased by 10 minutes, what would be the percentage increase in speed?

Tip: When dealing with speed, time, and distance, remember that speed is inversely proportional to time when distance is constant.