Michel travelled from New York to New Jersy covering total distance of 250 mile in 8 h partly by car at 30 mile/h and rest by train at 35 mile/h. The distance travelled by car is :

Options

A. 150 mile
B. 80 mile
C. 220 mile
D. 180 mile

Answer

To solve the problem, we need to determine the distance Michel traveled by car. Let's break it down step by step.

### Step 1: Define Variables
Let the distance traveled by car be \( x \) miles. Therefore, the distance traveled by train will be \( 250 - x \) miles, since the total distance is 250 miles.

### Step 2: Set Up the Time Equation
We know the speeds:
- Speed of the car = 30 miles/hour
- Speed of the train = 35 miles/hour

Using the formula for time, which is \( \text{Time} = \frac{\text{Distance}}{\text{Speed}} \), we can express the time taken for each part of the journey:

- Time taken by car = \( \frac{x}{30} \)
- Time taken by train = \( \frac{250 - x}{35} \)

### Step 3: Write the Total Time Equation
The total time for the journey is given as 8 hours. Therefore, we can set up the equation:

\[ \frac{x}{30} + \frac{250 - x}{35} = 8 \]

### Step 4: Solve the Equation
To solve this equation, we will first find a common denominator. The least common multiple (LCM) of 30 and 35 is 210.

Now, we can rewrite the equation:

\[ \frac{7x}{210} + \frac{6(250 - x)}{210} = 8 \]

This simplifies to:

\[ \frac{7x + 1500 - 6x}{210} = 8 \]

Combining like terms gives:

\[ \frac{x + 1500}{210} = 8 \]

### Step 5: Eliminate the Denominator
Multiply both sides by 210 to eliminate the fraction:

\[ x + 1500 = 1680 \]

### Step 6: Solve for \( x \)
Now, isolate \( x \):

\[ x = 1680 - 1500 \]
\[ x = 180 \]

### Conclusion
The distance traveled by car is \( 180 \) miles.

---