In a 500 m race, A and B's speed ratio is 3 : 4. A gets a start of 140 m. By how many metres does A win?

Problem restatement
A starts 140 m ahead; A's speed : B's speed = 3 : 4. Find the distance by which A wins the 500 m race.

Given data

• A's required run = 500 − 140 = 360 m.
• Speeds: v_A : v_B = 3 : 4.

Concept/Approach
Compare positions at the instant A finishes: compute B's covered distance by then.

Step-by-step calculation
Time for A = 360 ÷ (3k) = 120 ÷ k B's distance in this time = (4k) × (120/k) = 480 m Margin (A over B) = 500 − 480 = 20 m

Verification/Alternative
Alternatively, compute times to finish: A = 120/k, B = 500/(4k) = 125/k ⇒ A indeed finishes first by 5/k seconds.

Final Answer
20 m