Discussion
Trucks (10 m long) and cars (5 m long) go on a single lane bridge. There must be a gap of at least 20 m after each truck and a gap of at least 15 m after each car. Trucks and cars travel at a speed of 36 km/h. If cars and trucks go alternately, what is the maximum number of vehicles that can use the bridge in one hour?
Answer: A
At most 1440 vehicles can use the bridge in an hour.
With trucks and cars alternating, each truck-car pair takes up its own length plus its required gap:
\[ \begin{aligned} \text{pair} &= (10 + 20) + (5 + 15) = 50\ \text{m} \\ 36\ \text{km/h} &= 10\ \text{m/s} \end{aligned} \]
So one pair passes every 5 seconds, and in 3600 seconds
\[ \frac{3600}{5} = 720\ \text{pairs} = 1440\ \text{vehicles} \]
720 is the number of pairs, which counts each truck-car pair as one vehicle. 1200 and 600 allow more road per vehicle than the rules need: 30 m per vehicle gives 1200 and 60 m per vehicle gives 600.
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