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# Coordinating Arrival

Alex wants to take his two sons to visit their grandmother,living 33 kilometers away.

His motorcycle can run 25 kilometers per hour if he rides alone, but the speed drops to 20 kph if he carries one passenger and he cannot carry two.

The walking speed of each of the boys is 5 kph.

How can the three of them reach grandmother’s house in 3 hours?

Note by Danish Ahmed
2 years, 2 months ago

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1. Carry two people on motorcycle for 1.2 hours. After 1.2 hours, one person is at 6 km, two people are at 24 km, and the motorcycle is at 24 km.
2. Return back with motorcycle for 0.6 hours. After 1.8 hours, two people are at 9 km, one person is at 27 km, and the motorcycle is at 9 km.
3. Carry two people on motorcycle for 1.2 hours. After 3 hours, all three people are at 33 km, along with the motorcycle.

- 2 years, 2 months ago

Please note that it isn't necessary to give the time required to reach granny's house. If Alex takes one boy to a distance x and returns alone to the other boy who has covered some distance already, takes him to the house to find that all three have arrived simultaneously then: x/20+x/40+(33-x/4-x/8)/20=x/20+(33-x)/5 which gives x=24 km and total time required x/20+(33-x)/5=3 hrs.

- 2 years, 2 months ago

Oh, that would make a really interesting problem :)

Staff - 2 years, 2 months ago