Sumit drove at the speed of 45km/h from home to a resort.Returning over the same route,he got stuck in traffic and took an hour longer.Also,he could drive only the speed of 40 km/h.How many kilometres did he drive each way?

Options

A. 250 km
B. 360 km
C. 375 km
D. None of these

Answer

To solve the problem step by step, we will define the variables and set up equations based on the information provided.

### Step 1: Define the Variables
Let the distance from Sumit's home to the resort be \( d \) kilometers.

### Step 2: Determine the Time Taken for Each Journey
- When Sumit drives to the resort at a speed of 45 km/h, the time taken (let's call it \( t \)) can be expressed as:
\[ t = \frac{d}{45} \]
- On the return trip, he drives at a speed of 40 km/h and takes an hour longer than the outward journey, so the time taken for the return trip is:
\[ t + 1 = \frac{d}{40} \]

### Step 3: Set Up the Equation
Now we have two equations:
1. \( t = \frac{d}{45} \)
2. \( t + 1 = \frac{d}{40} \)

Substituting the first equation into the second gives:
\[ \frac{d}{45} + 1 = \frac{d}{40} \]

### Step 4: Solve for \( d \)
To eliminate the fractions, we can multiply through by the least common multiple of 45 and 40, which is 360:
\[ 360 \left( \frac{d}{45} \right) + 360 \cdot 1 = 360 \left( \frac{d}{40} \right) \]
This simplifies to:
\[ 8d + 360 = 9d \]
Rearranging gives:
\[ 360 = 9d - 8d \]
\[ 360 = d \]

### Step 5: Conclusion
Thus, the distance Sumit drove each way is:
\[ d = 360 \text{ kilometers} \]

### Summary
Sumit drove 360 kilometers to the resort and 360 kilometers back home.

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