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John, Chris and Adrian are stuck in traffic on a bridge in LA. They must be arrive at the office the soonest possible for a very important meeting but they are 30 miles away!
At the edge of the road they find a motor-bike and a racing bicycle, which they decide to “borrow”, as a last desperate effort to finally get to the office on time!
The motorbike is quite old and can only run at a maximum speed of 30 miles per hour, while the bicycle can run at 20 miles per hour. Fortunately, all three are very fit and can also run at 10 miles per hour. If they want, they can leave the motorbike or the bicycle at the edge of the street, for someone else to take it. What is the minimum time they will require to reach the office (all three of them), assuming that the streets are always open for motorbikes / bicycles and joggers?
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The fastest way for the three men to reach the office is to traverse the distance to the office using the motoribike, but this is impossible since it is obvious from the context that each one can use only one mean of transportation. The second fastest way to pass that distance is to cover it using the two fastest means of transportation (the motorbike and the bicycle), but in this way only two men can use these two means and the third one has to traverse the distance to the office running, so the time of arrival of the three men will be extended to 3 hours (the longest time of the journy). Finally the third fastest way to cover that distance is by using all the three means (the motorbike, the bicycle and running) in the journy of all the three men. And this can be done as follow:
They divide the whole distance to the office (30 mi) into three subintervals each of length 10 mi with a station at the end of each subinterval and at the start of the journy they let one of them run while the other two stay at the starting point. Since the speeds of the motorbike, bicycle and running are 30 mi/h, 20 mi/h and 10 mi/h respectively. After 0.5 hour the man which riding the bicycle starts to drive at its maximum speed (20 mi/h) and when 0.75 hour has elapsed the one with the motorbike start driving (at maximum speed also) in this way all of them will arrive at the first station on the same time. Then they exchange the means of transportations (e.g. the running man ride the bicycle, the man with the bicycle takes the motorbike and the one with the motorbike starts running) and they repeat the same procesures mentioned above in this station, so they will arrive at the same time in the second station where they repeat the same proccess again to reach the final station which is the office. In this way each of them will use the three means of transportations and the time taken for the journy (neglecting the exchange time) will be:
Note: someone may wonder, why we did not divide the distance into more then three subintervals, we may have better time?! No the result will be the same since each means of transportation will be used in the same number of subintervals.
Q.E.F
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Correct! Great job!!
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