The main street in a town has a linked traffic system consisting of six consecutive sections, each a multiple of 1/8th of a kilometre in length, and each terminating in a traffic light.
These lights have a 26-second cycle, which can be considered as 13 seconds on red and 13 on green. The lights are synchronised so that a vehicle travelling at 30 kmph will pass each light at the same point in its cycle. Albert, has studied the system and reckons he can drive faster than 30 kmph and still get through the entire system without crossing a red light. Recently, he set up an experiment with the help of two friends, Robert and Hubert. All three entered the first section simultaneously, Albert travelling at 30, Hubert at 50 and Robert at 75 kmph, with the first traffic light turning green three seconds later. Robert got through the whole system in less than two minutes without being stopped. However, he thought he had been lucky, as he arrived at the last light just as it changed to red. Hubert ran out of petrol after the third light, and in any case would have been stopped at the second light had he not lost 10 seconds due to a delay in the second section. What were the lengths of each of the six sections?
It does not seem to have a solution. Are you sure about the conditions? |
I think there is. I got total distance 20/8 km. The first section is 9/8 km. The rest just took more time. |
The total distance 20/8. Sections are 4/8, 3/8, 5/8, 3/8, 3/8, 2/8 kilimeters. Since Robert bearly get through the last traffic light, we can consider it took a little less than 2 minutes. |
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