Discussion
In a race of 200 metres, A can give a start of 10 metres to B, and C can give a start of 20 metres to A. The start that C can give to B, in the same race, is
Answer: B
In these problems the two players are compared by the scores they reach in the same time, so their rates are in the ratio of those scores.
Chain the two statements through A.
\[ A\,200 : B\,190, \qquad C\,200 : A\,180 \]
When C runs 200, A runs 180; and when A runs 180, B runs
\[ 180 \times \frac{190}{200} = 171 \text{ m} \]
\[ \text{C can give B} = 200 - 171 = 29 \text{ m} \]
Adding the two starts gives 30 m, which is close but wrong: B's 10 m deficit is measured over 200 m, and here B only runs 180.
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