In a 100 m race, A can give B 10 m and C 28 m. In the same race B can give C:

In the 100m race:

1. A can give B a 10m head start. This means that when A runs 100m, B runs 90m.
2. A can also give C a 28m head start. This means that when A runs 100m, C runs 72m.

We can use these ratios to find out how much of a head start B can give C.

First, we need to find out how far B runs when A runs 72m (the distance C runs in a 100m race against A). We can set up a proportion to solve this:

90m (B's distance when A runs 100m) / 100m (A's distance) = x (B's distance when A runs 72m) / 72m (A's distance)

Solving for x gives us x = 90m * 72m / 100m = 64.8m

This means that when A runs 72m, B runs 64.8m.

Therefore, in a 100m race, B can give C a head start of 100m - 64.8m = 35.2m.

In a 100 m race, A can give B a 10 m lead, which means A runs 100 m while B runs 90 m.

Similarly, A can give C a 28 m lead, which means A runs 100 m while C runs 72 m.

To find out how much of a lead B can give C, we need to compare their speeds.

The speed ratio of A to B is 100:90 and the speed ratio of A to C is 100:72.

To find the speed ratio of B to C, we can set up the equation 90/100 = x/72, where x is the distance B runs when C runs 72 m.

Solving for x gives us x = 90 * 72 / 100 = 64.8 m.

So, in a 100 m race, B can give C a lead of 100 - 64.8 = 35.2 m.

In a 100 m race, if A can give B a 10 m lead, it means A is faster than B and can finish the race 10 m ahead of B. Similarly, if A can give C a 28 m lead, it means A is faster than C and can finish the race 28 m ahead of C.

Now, if we compare B and C, we know that A finishes 10 m ahead of B and 28 m ahead of C. Therefore, the difference between B and C would be the difference between the distances A can finish ahead of them, which is 28 m - 10 m = 18 m.

So, in the same 100 m race, B can give C an 18 m lead.

In the 100 m race, A can give B a 10 m lead, which means A runs 100 m while B runs 90 m.

Similarly, A can give C a 28 m lead, which means A runs 100 m while C runs 72 m.

To find out how much of a lead B can give C, we need to compare their speeds.

The speed ratio of A to B is 100:90 and the speed ratio of A to C is 100:72.

To find the speed ratio of B to C, we can set up the following equation:

(90/100) = (x/72)

Solving for x gives us x = 65.6

This means B can give C a lead of 100 - 65.6 = 34.4 m.

So, in a 100 m race, B can give C a 34.4 m lead.