One day, Mr. Richards started 30 minutes late from home and reached his office 50 minutes late. While driving 25% slowe than his usual speed. How much time in minutes does Mr. Richard usually take to reach his office from home?

Options

A. 20
B. 40
C. 60
D. 80

Answer

To solve the problem step by step, we can follow this approach:

### Step 1: Understand the problem
Mr. Richards started 30 minutes late and reached his office 50 minutes late. This means he took an extra 20 minutes on the road.

**Hint:** Identify the extra time taken by Mr. Richards due to starting late and arriving late.

### Step 2: Define variables
Let:
- \( t \) = usual time taken by Mr. Richards to reach his office (in minutes)
- \( d \) = distance from home to office
- \( s \) = usual speed of Mr. Richards

### Step 3: Establish the relationship between time, speed, and distance
The formula for speed is:
\[ \text{Speed} = \frac{\text{Distance}}{\text{Time}} \]
From this, we can express time as:
\[ t = \frac{d}{s} \]

**Hint:** Remember the relationship between speed, distance, and time.

### Step 4: Determine the new speed
Mr. Richards drove 25% slower than his usual speed. Therefore, his new speed \( s' \) is:
\[ s' = s - 0.25s = 0.75s = \frac{3s}{4} \]

**Hint:** Calculate the new speed based on the percentage decrease.

### Step 5: Determine the new time taken
Since Mr. Richards took an extra 20 minutes, the new time taken \( t' \) is:
\[ t' = t + 20 \]

### Step 6: Set up the equation using the new speed
Using the formula for speed, we can express the new time in terms of distance and new speed:
\[ t + 20 = \frac{d}{s'} = \frac{d}{\frac{3s}{4}} = \frac{4d}{3s} \]

**Hint:** Substitute the new speed into the time formula.

### Step 7: Substitute distance \( d \)
We know from the original time that:
\[ d = st \]
Substituting this into the equation gives:
\[ t + 20 = \frac{4(st)}{3s} \]
This simplifies to:
\[ t + 20 = \frac{4t}{3} \]

**Hint:** Replace \( d \) with \( st \) to simplify the equation.

### Step 8: Solve for \( t \)
Now, we can solve the equation:
1. Multiply both sides by 3 to eliminate the fraction:
\[ 3(t + 20) = 4t \]
\[ 3t + 60 = 4t \]
2. Rearranging gives:
\[ 60 = 4t - 3t \]
\[ 60 = t \]

**Hint:** Rearranging the equation helps isolate \( t \).

### Conclusion
Mr. Richards usually takes **60 minutes** to reach his office from home.

**Final Answer:** 60 minutes