Please read the question carefully and answer the questions carefully
In a 500 metre race, X runs at 5 m/s. 'Y' is already 314 meters ahead of 'X' when the race starts. If 'Y' beats X by 7 seconds then what is Y's speed?

Options
2 m/s

2.5 m/s

3.5 m/s

3 m/s

Let's solve the problem step by step.

### Given:
- **Distance of the race**: 500 meters
- **Speed of X**: 5 m/s
- **Y's head start**: 314 meters
- **Y beats X by**: 7 seconds

### Step 1: Calculate the time taken by X to complete the race.
X has to cover the full distance of 500 meters.

\[
\text{Time taken by X} = \frac{\text{Distance}}{\text{Speed}} = \frac{500 \text{ meters}}{5 \text{ m/s}} = 100 \text{ seconds}
\]

### Step 2: Calculate the time taken by Y to finish the race.
Since Y beats X by 7 seconds, Y completes the race in 7 seconds less than X.

\[
\text{Time taken by Y} = 100 \text{ seconds} - 7 \text{ seconds} = 93 \text{ seconds}
\]

### Step 3: Calculate Y's speed.
Y has a head start of 314 meters, so Y only needs to cover the remaining distance.

\[
\text{Distance Y has to cover} = 500 \text{ meters} - 314 \text{ meters} = 186 \text{ meters}
\]

Now, Y covers 186 meters in 93 seconds.

\[
\text{Speed of Y} = \frac{\text{Distance}}{\text{Time}} = \frac{186 \text{ meters}}{93 \text{ seconds}} = 2 \text{ m/s}
\]

### Conclusion:
Y's speed is **2 m/s**.

### Answer:
The correct option is **2 m/s**.

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Would you like more details, or do you have any questions about this solution?

Here are five related questions for further practice:

1. If X ran at 6 m/s instead, how much time would Y need to beat X by the same 7 seconds?
2. What would Y's speed be if they beat X by 10 seconds instead?
3. If Y was only 200 meters ahead at the start, what would Y's speed need to be to still beat X by 7 seconds?
4. How much of a head start would Y need if they ran at 1.5 m/s to still beat X by 7 seconds?
5. If X and Y both started at the same point, how fast would Y need to run to tie with X?

**Tip**: Always break down the problem into smaller steps and solve systematically to avoid confusion and errors.

In a 500 metre race, X runs at 5 m/s. 'Y' is already 314 meters ahead of 'X' when the race starts. If 'Y' beats X by 7 seconds then what is Y's speed? Options: 2 m/s, 2.5 m/s, 3.5 m/s, 3 m/s

Learn how to calculate the speed of Y in a 500 meter race where Y starts 314 meters ahead and beats X by 7 seconds. This problem involves understanding distance, speed, and time, and is suitable for students in Grades 7-9.

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