A runs 1$ \dfrac{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?
200 m
300 m
270 m
160 m
Explanation:
Ratio of the speeds of A and B =$ \dfrac{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(\dfrac{5}{2} \times 80\right) $m= 200 m.
$\therefore$ Winning post is 200 m away from the starting point.