Mr. X runs 5 times as fast as Mr. Y. If Mr. X gives Mr. Y a start of 80 meters, how far must the goal on the race course be so that Mr. X and Mr. Y reach it at the same time?
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 100 m
Let the goal be d metres from the starting point of Mr. X. Mr. Y has a start of 80 m, so he runs \( d-80 \) metres. They take the same time, so their distances are in the ratio of their speeds.
\( \displaystyle \frac{d}{d-80}=\frac{5}{1} \)
\( \displaystyle d=5d-400 \)
\( \displaystyle d=100 \)
The goal must be 100 m away.
Shortcut: In the same time X covers 5 parts and Y covers 1. The 80 m start is the difference of 4 parts, so 1 part = 20 m and the goal is 5 parts = 100 m.