Problem

26. 一只野兔逃出80步后猎狗才追它,野兔跑 8步的路程猎狗只需跑3步,猎狗跑4步的时间兔子能跑9 步。猎狗至少要跑多少步才能追上野兔?
解:狗跑12步的路程等于兔跑32步的路程,狗跑12步的时间等于兔跑27步的时间。所以兔每跑27步,狧 追上5步(兔步),狗要追上80步(兔步)需跑[27× $(80 \div 5)+80] \div 8 \times 3=192$ (步)。
27.甲、乙两人在铁路旁边以同样的速度沿铁路方向相向而行, 恰好有一列火车开来, 整个火车经过甲身 用了18秒,2分后又用15秒从乙身边开过。问:
(1) 火车速度是甲的速度的几倍?

Answer

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Answer

4. Final Answer: \(\boxed{\frac{20}{17}}\) times A's speed

Steps

Step 1 :1. Set up the equation to find the relationship between the distance the train travels in 18 seconds and 15 seconds: \(\frac{distance_{train_{18s}}}{distance_{train_{15s}}} = \frac{18 \times speed_{train}}{15 \times speed_{train}}\)

Step 2 :2. Simplify the equation to find the relationship between the train's speed and A's speed: \(\frac{distance_{train_{120s}}}{distance_{A_{120s}} + distance_{train_{18s}}} = \frac{120 \times speed_{train}}{120 \times speed_{A} + 18 \times speed_{train}}\)

Step 3 :3. Solve the simplified equation to find the relationship between the train's speed and A's speed: \(\frac{20 \times speed_{A}}{17 \times speed_{train}}\)

Step 4 :4. Final Answer: \(\boxed{\frac{20}{17}}\) times A's speed

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