In a 100 m race, Tina beats Mina by 20 m, and in the the same race, Mina beats Rita by 10 m By what distance does Tina beat Rita ?

Answer

To solve the problem step by step, we can break it down as follows:

### Step 1: Understand the Race Distances
In a 100 m race:
- Tina beats Mina by 20 m. This means when Tina finishes the race (100 m), Mina has only run 80 m.
- Mina beats Rita by 10 m. This means when Mina finishes the race (100 m), Rita has only run 90 m.

### Step 2: Determine the Distances Covered by Each Runner
1. **Tina's distance when she finishes the race**: 100 m
2. **Mina's distance when Tina finishes**: 80 m
3. **Rita's distance when Mina finishes**: 90 m

### Step 3: Calculate the Distance Rita Runs When Tina Finishes
Since Mina runs 80 m when Tina runs 100 m, we need to find out how far Rita runs in the same time.

- When Mina runs 100 m, Rita runs 90 m.
- Therefore, when Mina runs 80 m, Rita runs:

\[ \text{Rita's distance} = \left(\frac{90}{100}\right) \times 80 = 72 \text{ m} \]

### Step 4: Calculate the Distance by Which Tina Beats Rita
Now, we can determine how much distance Tina beats Rita by:

- When Tina finishes the race (100 m), Rita has run 72 m.
- Thus, the distance by which Tina beats Rita is:

\[ \text{Distance Tina beats Rita} = 100 \text{ m} - 72 \text{ m} = 28 \text{ m} \]

### Final Answer
Tina beats Rita by 28 m.

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