Ram walks at a speed of 24 km/h. Today the day was very hot so walked at 5/6 of his average speed. He arrived his school 20 minutes late. Find the usual time he takes to cover the distance between his school and home?

Let's solve the problem step by step.

### Step 1: Understand the problem
- **Ram's usual speed:** 24 km/h
- **Reduced speed today:** \( \frac{5}{6} \) of his usual speed
- **Time late:** 20 minutes

### Step 2: Calculate the reduced speed
The reduced speed today is:
\[
\text{Reduced speed} = \frac{5}{6} \times 24 = 20 \text{ km/h}
\]

### Step 3: Let the usual time taken be \( t \) hours
- The usual time to travel from home to school at 24 km/h is \( t \) hours.
- The distance from home to school can be calculated as:
\[
\text{Distance} = \text{Speed} \times \text{Time} = 24 \times t \text{ km}
\]

### Step 4: Calculate the time taken today at the reduced speed
- The time taken today at 20 km/h would be:
\[
\text{Time taken today} = \frac{\text{Distance}}{\text{Reduced speed}} = \frac{24t}{20} = 1.2t \text{ hours}
\]

### Step 5: Use the information about being late
- According to the problem, he was 20 minutes late. This means:
\[
1.2t = t + \frac{20}{60}
\]
- Simplifying the equation:
\[
1.2t - t = \frac{1}{3} \text{ hours}
\]
\[
0.2t = \frac{1}{3} \text{ hours}
\]
\[
t = \frac{1}{3} \times \frac{1}{0.2} = \frac{1}{3} \times 5 = \frac{5}{3} \text{ hours}
\]

### Step 6: Convert the time to minutes
\[
t = \frac{5}{3} \times 60 = 100 \text{ minutes}
\]

So, the usual time Ram takes to cover the distance between his school and home is **100 minutes**.

Would you like more details, or do you have any questions? Here are some related questions you might be interested in:

1. How do you convert time from hours to minutes in general?
2. What if the reduced speed was different, how would it affect the result?
3. How do you solve problems with different kinds of speed changes?
4. Can this problem be solved using ratios?
5. What if Ram arrived earlier than usual instead of later?

**Tip:** Always convert units consistently when solving distance-speed-time problems to avoid mistakes.

Learn how to calculate Ram's usual time to cover the distance between his school and home. This problem involves speed, distance, and time calculations, where Ram walks at a reduced speed and arrives 20 minutes late. Suitable for Grades 7-9 students.

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