Question

A runs $1\frac{2}{3}$ times as fast as B. If A gives B a start of 80 m, how far must the winning post be so that A and B might reach it at the same time?

• A. 200 m
• B. 300 m
• C. 270 m
• D. 160 m

Answer 1

Answer: (A)

200 m

Ratio of the speeds of A and B $=\frac{5}{3}:1=5:3.$
Thus, in race of 5 m, A gains 2 m over B.
2 m are gained by A in a race of 5 m.
80 m will be gained by A in race of $\left(\begin{array}{c}\frac{5}{2}\times 80\end{array}\right)m=200m.$
$\therefore$ Winning post is 200 m away from the starting point.