Shamim had to travel 420 km in 8 hours. If he travelled at an average speed of 60 km/h and took two breaks in between, the shorter break being one-third the duration of the longer, how many minutes was the longer break for?
(a)45
(b)30
(c)40
(d)35

Options

A. 45
B. 30
C. 40
D. 35

Answer

To solve the problem step by step, we can follow these calculations:

### Step 1: Calculate the time taken to travel 420 km at 60 km/h
To find the time taken to travel a certain distance, we use the formula:
\[ \text{Time} = \frac{\text{Distance}}{\text{Speed}} \]
Here, the distance is 420 km and the speed is 60 km/h.

\[ \text{Time} = \frac{420 \text{ km}}{60 \text{ km/h}} = 7 \text{ hours} \]

**Hint:** Remember that time is calculated by dividing distance by speed.

### Step 2: Determine the total time available for travel and breaks
Shamim has a total of 8 hours for his journey. Since he took 7 hours to travel, we can find the total time spent on breaks.

\[ \text{Total time for breaks} = \text{Total time} - \text{Travel time} = 8 \text{ hours} - 7 \text{ hours} = 1 \text{ hour} \]

**Hint:** Subtract the travel time from the total time to find the time left for breaks.

### Step 3: Convert the total break time into minutes
Since we need the break time in minutes, we convert 1 hour into minutes.

\[ 1 \text{ hour} = 60 \text{ minutes} \]

**Hint:** Remember that 1 hour equals 60 minutes.

### Step 4: Set up the relationship between the longer and shorter breaks
Let the duration of the longer break be \( x \) minutes. According to the problem, the shorter break is one-third of the longer break.

\[ \text{Shorter break} = \frac{x}{3} \]

### Step 5: Write the equation for total break time
The total break time is the sum of the longer and shorter breaks.

\[ x + \frac{x}{3} = 60 \]

### Step 6: Solve for \( x \)
To solve the equation, first, find a common denominator. The common denominator for 1 and 3 is 3.

\[ \frac{3x}{3} + \frac{x}{3} = 60 \]
\[ \frac{4x}{3} = 60 \]

Now, multiply both sides by 3 to eliminate the fraction:

\[ 4x = 180 \]

Now, divide by 4:

\[ x = \frac{180}{4} = 45 \]

### Conclusion
The duration of the longer break is 45 minutes.

**Final Answer:** (a) 45