Bunuel wrote:
A runs 25% faster than B and is able to allow B a lead of 7 meters to end a race in dead heat. What is the length of the race?
A. 10 meters
B. 15 meters
C. 25 meters
D. 35 meters
E. 45 meters
Let the length of the race be \(d\), B runs \((d-7)\) meters and A runs \(d\) meters, in \(s\) mph and \(1.25s\) mph respectively.
\(time = \frac{distance}{speed}\)
Time taken by A = \(\frac{d}{1.25s}\)
Time taken by B = \(\frac{d-7}{s}\)
Since the race was a dead heat \(\frac{d}{1.25s} = \frac{d-7}{s}\)
\(ds = 1.25ds - 8.75s\)
\(d = 1.25d - 8.75\)
\(d = \frac{8.75}{0.25} = 35\).