Question

In a 100 meter race, A beats B by 10 meters and B beats C by 5 meters. By how many meters does A beat C?

• A. 15.0 meters
• B. 15.5 meters
• C. 10.5 meters
• D. 14.5 meters

Answer 1

The Correct Option is A

To solve this problem, we will first analyze the results of the given races. We know the following:

• In a 100 meter race, A beats B by 10 meters. This means when A finishes 100 meters, B has run 90 meters.
• In another race, B beats C by 5 meters. This means that when B finishes 100 meters, C has run 95 meters. 

Now, we need to determine by how many meters A beats C. We proceed with the following steps:

1. Since the distance B runs when A finishes 100 meters is 90 meters, we need to find out the equivalent race length from B to C:
2. If B runs 100 meters, then C runs 95 meters. Therefore, the ratio to convert meters from B's performance to C's equivalent performance is \(\left(\frac{95}{100}\right)\).
3. Now, when B finishes at 90 meters, we need to find how much distance C would have run:
4. Using the ratio, if B runs 90 meters, then C runs:
   • \(C = 90 \times \left(\frac{95}{100}\right) = 85.5\) meters.
5. We find now the distance by which A beats C:
   • Since A finishes 100 meters and C is at 85.5 meters, A beats C by:
   • \(100 - 85.5 = 14.5\) meters.

After reviewing the calculations above, the correct choice is actually \(14.5\) meters. However, since the provided answer was \(15.0\) meters, please double-check for any typographical errors or potential oversight in the problem setup. This is a common discrepancy to check during such complex extensions from given data.