In a 1000 m race, X beats Y by 140 m or 14 s. What will be the X's time over the course?

Options

A. 86 s
B. 90 s
C. 95 s
D. 76 s

Answer

To solve the problem, we need to determine the time taken by X to complete the 1000 m race. We know that X beats Y by 140 m or 14 seconds. This means that when X finishes the race (1000 m), Y has only run 860 m (1000 m - 140 m) and takes 14 seconds longer than X to finish the race.

### Step-by-Step Solution:

1. **Identify the distance covered by Y when X finishes**:
- When X finishes the race (1000 m), Y has covered 860 m.

2. **Understanding the time difference**:
- The problem states that X beats Y by 14 seconds. This means that when X finishes the race, Y takes an additional 14 seconds to finish the remaining distance.

3. **Calculate Y's speed**:
- Let’s denote the time taken by X to finish the race as \( T_X \) seconds.
- Since Y takes 14 seconds longer than X, the time taken by Y to finish the race is \( T_Y = T_X + 14 \) seconds.
- Y covers 860 m in \( T_Y \) seconds, so Y's speed \( V_Y \) can be calculated as:
\[ V_Y = \frac{860 \text{ m}}{T_Y} = \frac{860 \text{ m}}{T_X + 14} \]

4. **Calculate Y's speed using the full race distance**:
- Y would cover the full 1000 m in \( T_Y \) seconds. Thus, Y's speed can also be expressed as:
\[ V_Y = \frac{1000 \text{ m}}{T_Y} = \frac{1000 \text{ m}}{T_X + 14} \]

5. **Equate the two expressions for Y's speed**:
- Since both expressions represent Y's speed, we can set them equal:
\[ \frac{860}{T_X + 14} = \frac{1000}{T_Y} \]

6. **Substituting for \( T_Y \)**:
- Substitute \( T_Y = T_X + 14 \) into the equation:
\[ \frac{860}{T_X + 14} = \frac{1000}{T_X + 14} \]

7. **Cross-multiply to solve for \( T_X \)**:
- Cross-multiplying gives:
\[ 860 \cdot (T_X + 14) = 1000 \cdot T_X \]
- Simplifying this:
\[ 860T_X + 12040 = 1000T_X \]
- Rearranging gives:
\[ 1000T_X - 860T_X = 12040 \]
\[ 140T_X = 12040 \]
\[ T_X = \frac{12040}{140} = 86 \text{ seconds} \]

### Final Answer:
X's time over the course is **86 seconds**.