A runs 25% faster than B and is able to give him a start of 7 m to end a race in a dead heat. What is the length of the race?

Step 1: Let's assume the speed of B is x m/s. Then the speed of A will be 1.25x m/s (since A is 25% faster than B).

Step 2: Let's assume the time taken to finish the race is t seconds. Since they finish the race at the same time, we can say that the time taken by A and B is the same.

Step 3: The distance covered by B in time t is the length of the race, which we can denote as R. So, B's speed x time = distance, or x*t = R.

Step 4: The distance covered by A in the same time t is the length of the race plus the 7m head start given to B. So, A's speed x time = distance, or 1.25x*t = R + 7.

Step 5: Now we have two equations (xt = R and 1.25xt = R + 7) and we can solve them simultaneously to find the values of R and t.

Step 6: Subtract the first equation from the second to get 0.25x*t = 7. Solving for t, we get t = 7 / 0.25x = 28/x.

Step 7: Substitute t = 28/x into the first equation to get x*(28/x) = R. Simplifying, we find R = 28m.

So, the length of the race is 28 meters.