A train X starts from a place at a speed of 50 km/hr. After one hour, another train Y starts from the same place at a speed of 70 km/hr. After how much time will Y cross X?

Options

A. 3 hrs
B. ` 2 (3)/(4)` hrs
C. ` 3 (1)/(2) `hrs
D. ` 2 (1)/(4)` hrs

Answer

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

### Step 1: Define the Variables
Let \( X \) be the time in hours after which train Y crosses train X.

### Step 2: Calculate the Distance Covered by Train X
Train X starts first and travels for \( X + 1 \) hours (since it started 1 hour earlier). The distance covered by train X can be calculated using the formula:
\[ \text{Distance} = \text{Speed} \times \text{Time} \]
So, the distance covered by train X is:
\[ \text{Distance}_X = 50 \times (X + 1) = 50X + 50 \text{ km} \]

### Step 3: Calculate the Distance Covered by Train Y
Train Y starts 1 hour later, so it travels for \( X \) hours. The distance covered by train Y is:
\[ \text{Distance}_Y = 70 \times X = 70X \text{ km} \]

### Step 4: Set Up the Equation
Since we want to find out when train Y crosses train X, we set their distances equal to each other:
\[ 50X + 50 = 70X \]

### Step 5: Solve the Equation
Rearranging the equation gives:
\[ 70X - 50X = 50 \]
\[ 20X = 50 \]
Now, divide both sides by 20:
\[ X = \frac{50}{20} = \frac{5}{2} \text{ hours} \]

### Step 6: Convert to Mixed Number
To convert \( \frac{5}{2} \) hours into a mixed number:
\[ \frac{5}{2} = 2 \frac{1}{2} \text{ hours} \]

### Conclusion
Train Y will cross train X after \( 2 \frac{1}{2} \) hours.

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