A man rides his vehicle at the rate of 36km/hr but stops for 12 minutes, to change parts at the end of every 14th km. What will be the time taken to cover a distance of 90 km?

Options

A. 6 hours 12 minutes
B. 2 hours 30 minutes
C. 3 hours 42 minutes
D. 5 hours 32 minutes

Answer

To solve the problem step by step, we will calculate the total time taken by the man to cover a distance of 90 km, considering his speed and the stoppages he makes.

### Step 1: Calculate the time taken to ride without stoppages
The speed of the man is given as 36 km/hr. To find the time taken to cover 90 km without any stoppages, we can use the formula:

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

Substituting the values:

\[ \text{Time} = \frac{90 \text{ km}}{36 \text{ km/hr}} = 2.5 \text{ hours} \]

### Step 2: Determine the number of stoppages
The man stops every 14 km. To find out how many times he stops while covering 90 km, we can calculate:

\[ \text{Number of stoppages} = \frac{90 \text{ km}}{14 \text{ km}} = 6.428 \text{ (approximately 6)} \]

Since he stops after completing each 14 km, he will stop 6 times (after 14 km, 28 km, 42 km, 56 km, 70 km, and 84 km).

### Step 3: Calculate the total distance covered before the last segment
After 6 stoppages, the total distance covered is:

\[ \text{Distance covered} = 14 \text{ km} \times 6 = 84 \text{ km} \]

This means he will cover the last 6 km without a stoppage.

### Step 4: Calculate the total stoppage time
Each stoppage lasts for 12 minutes. Therefore, the total stoppage time for 6 stoppages is:

\[ \text{Total stoppage time} = 6 \text{ stoppages} \times 12 \text{ minutes} = 72 \text{ minutes} = 1.2 \text{ hours} \]

### Step 5: Calculate the total time taken
Now, we add the riding time and the stoppage time together:

\[ \text{Total time} = \text{Riding time} + \text{Stoppage time} \]

\[ \text{Total time} = 2.5 \text{ hours} + 1.2 \text{ hours} = 3.7 \text{ hours} \]

### Step 6: Convert total time to hours and minutes
To convert 3.7 hours into hours and minutes:

\[ 3.7 \text{ hours} = 3 \text{ hours} + 0.7 \times 60 \text{ minutes} = 3 \text{ hours} + 42 \text{ minutes} \]

### Final Answer
The total time taken to cover a distance of 90 km is **3 hours and 42 minutes**.

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