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A student riding a bicycle on a 5 km one-way street takes 40 minutes to reach home. The student stopped for 15 minutes during the ride. Sixty vehicles overtook the student during the ride, and 45 vehicles overtook the student while the student was stopped. Assuming the student did not overtake any vehicle, the speed of the vehicle stream on that road (in km/h) is

1. 7.5
2. 12
3. 40
4. 60

Correct answer: 60

Solution

Let the vehicle stream speed be \(u\) km/h and bicycle speed be \(v\) km/h. During motion, overtaking rate is proportional to \(u-v\); during stoppage, it is proportional to \(u\). Using the two counts over the respective times gives \(u=60\) km/h.

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