Two friends started for a place one by motorcycle and the other by train. The speed of motorcycle is 30 km/h and that of train is 24 km/h. The first one takes 6 h 12 min to reach the destination. Find the time of reaching of second one?

Options

A. A)8h
B. B)7h25m
C. C)7h50m
D. D)7h45m

Answer

To solve the problem step by step, we will use the formula for distance, which is:

**Distance = Speed × Time**

### Step 1: Convert Time to Hours
The first friend takes 6 hours and 12 minutes to reach the destination. We need to convert this time into hours.

- 12 minutes can be converted to hours:
\[ 12 \text{ minutes} = \frac{12}{60} = \frac{1}{5} \text{ hours} \]

- Therefore, the total time in hours is:
\[ 6 \text{ hours} + \frac{1}{5} \text{ hours} = 6 + 0.2 = 6.2 \text{ hours} \]

### Step 2: Calculate the Distance
Now, we can calculate the distance traveled by the first friend using the speed of the motorcycle (30 km/h) and the time (6.2 hours).

- Using the formula:
\[ \text{Distance} = \text{Speed} \times \text{Time} = 30 \text{ km/h} \times 6.2 \text{ hours} = 186 \text{ km} \]

### Step 3: Calculate the Time Taken by the Second Friend
Now, we need to find the time taken by the second friend who travels by train at a speed of 24 km/h to cover the same distance of 186 km.

- Using the formula again, we rearrange it to find time:
\[ \text{Time} = \frac{\text{Distance}}{\text{Speed}} = \frac{186 \text{ km}}{24 \text{ km/h}} \]

### Step 4: Perform the Division
Now, we perform the division:
\[ \frac{186}{24} = 7.75 \text{ hours} \]

### Step 5: Convert Time to Hours and Minutes
To convert 7.75 hours into hours and minutes:
- The whole number part is 7 hours.
- The decimal part (0.75 hours) can be converted to minutes:
\[ 0.75 \text{ hours} \times 60 \text{ minutes/hour} = 45 \text{ minutes} \]

### Final Answer
Thus, the second friend takes **7 hours and 45 minutes** to reach the destination.

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