A runs 1(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 m300 m270 m160 mNone

Let's solve this step by step:

1. A runs 1(2/3) times as fast as B, which means A runs 5/3 times as fast as B.

2. If A gives B a start of 80 m, it means when B has run 80 m, A has run 0 m.

3. Since A runs 5/3 times as fast as B, when B runs x m, A runs 5/3*x m.

4. We need to find the distance to the winning post (x) so that A and B reach it at the same time. This means when B has run x m, A has also run x m.

5. But we know that when B has run 80 m, A has run 0 m. So when B has run x m, A has run (5/3*x - 80) m.

6. We set these two equal to each other to find x: x = 5/3*x - 80.

7. Solving for x, we get x = 240 m.

So, the winning post must be 240 m away for A and B to reach it at the same time. However, this option is not given in the question. So, the answer is 'None'.