Question

In a 10 km race. A, B, and C, each running at uniform speed, get the gold, silver, and bronze medals, respectively. If A beats B by 1 km and B beats C by 1 km, then by how many metres does A beat C?

• A. 1200
• B. 1900
• C. 3100
• D. 1500

Answer 1

The Correct Option is B

To determine by how many meters A beats C, we first need to analyze the relationships based on their speeds and time taken. Given:

1. A beats B by 1 km, meaning that when A finishes 10 km, B finishes 9 km.
2. B beats C by 1 km, meaning that when B finishes 10 km, C finishes 9 km. 

We can express time as distance/speed. Since all runners run at uniform speeds for the same amount of race time:

1. Let the speed of A be s_A. Then the time for A to complete 10 km is 10/s_A.
2. Let the speed of B be s_B. The time required by B for 9 km (B's position when A finishes) is 9/s_B = 10/s_A. Therefore, s_B = (9/10) × s_A.
3. Let the speed of C be s_C. The time required by C for 9 km (C's position when B finishes 10 km) is 9/s_C = 10/s_B. Therefore, s_C = (9/10) × s_B = (9/10)² × s_A.

We want to find how much distance C covers in the time A finishes 10 km:

1. Time taken by A to complete 10 km: 10/s_A.
2. Distance C runs in this time: 10 × s_C/s_A.
3. Substitute s_C: 10 × [(9/10)² × s_A]/s_A = 10 × (81/100) = 8.1 km.

A beats C by the difference between 10 km and 8.1 km:

1. Distance A beats C: 10 km - 8.1 km = 1.9 km which is 1900 meters.

The correct answer is thus: 1900 meters.