A bus covers distance in 3 hours 20 minutes at an average speed of 45 km/h. How long will it take to cover the same distance at a speed of 36 km/h ?

Answer

To solve the problem step by step, we will first determine the distance covered by the bus and then calculate the time it would take to cover the same distance at a different speed.

### Step 1: Convert the time from hours and minutes to hours only.
The bus covers a distance in 3 hours and 20 minutes. We need to convert 20 minutes into hours.

\[ 20 \text{ minutes} = \frac{20}{60} \text{ hours} = \frac{1}{3} \text{ hours} \]

So, the total time in hours is:

\[ 3 \text{ hours} + \frac{1}{3} \text{ hours} = \frac{9}{3} + \frac{1}{3} = \frac{10}{3} \text{ hours} \]

### Step 2: Calculate the distance covered by the bus.
Using the formula for distance:

\[ \text{Distance} = \text{Speed} \times \text{Time} \]

The speed of the bus is 45 km/h, and the time is \(\frac{10}{3}\) hours.

\[ \text{Distance} = 45 \text{ km/h} \times \frac{10}{3} \text{ hours} = 150 \text{ km} \]

### Step 3: Calculate the time taken to cover the same distance at a speed of 36 km/h.
We will use the same formula for distance, rearranged to find time:

\[ \text{Time} = \frac{\text{Distance}}{\text{Speed}} \]

Now, substituting the distance (150 km) and the new speed (36 km/h):

\[ \text{Time} = \frac{150 \text{ km}}{36 \text{ km/h}} = \frac{150}{36} \text{ hours} \]

### Step 4: Simplify the time calculation.
Now, simplify \(\frac{150}{36}\):

\[ \frac{150}{36} = \frac{25}{6} \text{ hours} \]

### Step 5: Convert the time from hours to hours and minutes.
To convert \(\frac{25}{6}\) hours into hours and minutes:

1. Divide 25 by 6:
- 25 divided by 6 is 4 with a remainder of 1.
- This means it is 4 hours and \(\frac{1}{6}\) of an hour.

2. Convert \(\frac{1}{6}\) hours into minutes:
- \(\frac{1}{6} \times 60 = 10\) minutes.

Thus, the total time taken is:

\[ 4 \text{ hours and } 10 \text{ minutes} \]

### Final Answer:
The time taken to cover the same distance at a speed of 36 km/h is **4 hours and 10 minutes**.

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