In a 500-meter race, the ratio of the speeds of two contestants, A and B, is 3:4. If A is given a head start of 140 meters, by how many meters does A win the race?

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Accepted Answer

The total distance of the race is **500 meters**, and A is given a head start of **140 meters**, so A needs to cover only:  
$$
500 - 140 = 360 \, 	ext{meters}.
$$

The ratio of the speeds of A and B is **3:4**, meaning that while A covers **3 meters**, B covers **4 meters**.

When A runs **360 meters**, the distance covered by B can be calculated as:  
$$
	ext{Distance covered by B} = \left(\frac{4}{3} 	imes 360ight) = 480 \, 	ext{meters}.
$$

Thus, when A reaches the finish line (500 meters), B has covered **480 meters**. The difference between their distances is:  
$$
500 - 480 = 20 \, 	ext{meters}.
$$

Therefore, **A wins the race by 20 meters**.

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