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On the Road

Four vehicles travelled on a road with constant velocities. The car overtook the scooter at 12 o'clock, then met the bike at 14.00 and the motorcycle at 16.00. The motorcycle met the scooter at 17.00 then it overtook the bike at 18.00. At what time did the bike and the scooter meet?

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There and Back

Brian swims at twice the speed that a river is flowing, downstream from one moored boat to another and back again, taking 12 minutes altogether. How long would it have taken him in still water?

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Escalator

At Holborn underground station there is a very long escalator. Two people are in a hurry and so climb the escalator as it is moving upwards, thus adding their speed to that of the moving steps. ... How many steps are there on the escalator?

Hike and Hitch

Stage: 4 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Fifteen students from Dr Challoner's Grammar School were told to go to a point 60 miles south. The only transport they could use was a car, which could only carry 5 students beside the driver (Thasan). Thasan took the students to their destination in 3 loads. As he left with the first 5, he ordered the remaining 10 to commence hiking along the road. He unloaded the first group some distance from the goal, with orders to hike the rest of the way. Then he returned until he met the remaining ten, picked up 5 of them, and took them part of the way along the route while the last 5 continued to walk. Finally he returned, picked up the last group and drove it the rest of the way. They all arrived at the same time. The students walked at a rate of 4 miles per hour without any pause for rest, while the car travelled at a speed of 40 miles per hour. How much time did the hiking save? (You can ignore the time spent in picking up and discharging passengers.)