In a 1-kilometer race, there are three participants: A, B, and C. A can give B a head start of 50 meters and C a head start of 69 meters (meaning they would finish at the same time). How many meters of head start can B give to C?

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The given information implies that the speeds of A, B, and C are in a specific ratio. Let's determine this ratio:

When A runs 1000 meters, B runs (1000 - 50) = 950 meters, and C runs (1000 - 69) = 931 meters in the same time.

Therefore, the **speed ratio** of A : B : C = 1000 : 950 : 931.

To find how much head start B can give to C, we need to analyze the relationship between B and C.

In a 950-meter race for B (which corresponds to their relative speeds):
- When B runs 950 meters, C runs 931 meters
- The difference is (950 - 931) = **19 meters**

This means in a 950-meter race, B can give C a head start of 19 meters, and they would finish at the same time.

Now, to find the head start in a 1000-meter (1 kilometer) race, we need to scale this value:

Head start = (19/950) × 1000 = **20 meters**

Therefore, in a 1-kilometer race, B can give C a head start of 20 meters and they would finish at the same time.

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