On a particular day, a man spent 12mins more driving to his office than driving home his average speed from home to his office was 40km/hr, from his office back home was 60km/hr. How far is the man's home from his office

Answer 1

Let's denote the distance from the man's home to his office as \( d \) kilometers.

We can find the time taken for each journey (to the office and back home) using the formula:

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

1. Time taken to drive to the office: \[ \text{Time to office} = \frac{d}{40} \text{ hours} \]

2. Time taken to drive back home: \[ \text{Time back home} = \frac{d}{60} \text{ hours} \]

According to the problem, the man spent 12 minutes more driving to his office than driving back home. To convert minutes into hours, we can use the conversion \( 12 \text{ mins} = \frac{12}{60} \text{ hours} = \frac{1}{5} \text{ hours} \).

We can set up the following equation based on the given information:

\[ \frac{d}{40} = \frac{d}{60} + \frac{1}{5} \]

Next, we need to eliminate the fractions by finding a common denominator. The least common multiple of 40 and 60 is 120. So we can multiply every term by 120 to eliminate the denominators:

\[ 120 \cdot \frac{d}{40} = 120 \cdot \frac{d}{60} + 120 \cdot \frac{1}{5} \]

This simplifies to:

\[ 3d = 2d + 24 \]

Now, we can isolate \( d \):

\[ 3d - 2d = 24 \] \[ d = 24 \]

Thus, the distance from the man's home to his office is \( \boxed{24} \) kilometers.