Official Solution:Three athletes A, B and C run a 1000 m race. When A is at a finish line, B is 50 m left to run and C is 88 m left to run. If all three athletes run at a constant speed, how many meters will C have to run to finish the race when B is at the finish line? A. \(19\)
B. \(36\)
C. \(38\)
D. \(39\)
E. \(40\)
By the time A covered 1000 m, B covered 950 m, and C covered 912 m.
The ratio of the distances covered by B and C in the
same time period is \(\frac{950}{912}\).
By the time B covered 1000 m, B covered
additional 50 m, and C covered
additional \(x\) m.
The ratio of the distances covered by B and C in the same time period is \(\frac{50}{x}\).
Since B and C run at constant speeds, then the ratio of the distances covered in the same period of time must be equal:
\(\frac{950}{912}=\frac{50}{x}\);
\(x=48\).
So, when B is at the finish line, C is left to run \(88-48=40\) m.
Answer: E