There are three routes leading to different places in a bus station. The first route starts every 15 minutes, the second route starts every 20 minutes, and the third route starts every 50 minutes. After the three routes start at the same time, how long does it take to start at the same time?

There are three routes leading to different places in a bus station. The first route starts every 15 minutes, the second route starts every 20 minutes, and the third route starts every 50 minutes. After the three routes start at the same time, how long does it take to start at the same time?

∵ 15 = 3 × 5, 20 = 2 × 2 × 5, 50 = 2 × 5 × 5, the least common multiple of ∵ 15, 20 and 50 is 2 × 2 × 3 × 5 × 5 = 300, ∵ at least 300 minutes later, the three lines will start at the same time

As shown in the figure, there are three ABC bus stations on the highway. A car starts from P, 10km away from a station, and runs at an average speed to C station at 8 a.m., and then leaves a station 25km after 15min
① Suppose that after starting XH, the car is YKM away from a station, and write the functional relationship between Y and X. ② when the car arrives at B station 200km away from a station, it is informed to arrive at C station 40km away from B station before 11:40 noon. If the car runs at the original speed, can it arrive on time? If it can, it will arrive at dozens of points? If not, how much should the speed be increased at least?

15 min = 1 / 4 h, vehicle distance = 25-10 = 15 km, then vehicle speed = 15 km / (1 / 4 h) = 60 km / h (1) function formula: y = 60 x + 10 (2) arrival time of station B: 200 = 60 x + 10, the solution is x = 3.1/6 hours = 3 hours, 10 minutes is 8:00 + 3 hours, 10 minutes = 11:10, the remaining 30 minutes is 11:40

A car drives from station a to station B at the speed of 40 km / h. when it starts, a bus just drives from station B to station a, and then every 15 minutes a bus drives from station B to station A. if the truck meets 6 buses on the way, the distance between station a and station B may be ()
A. 45 km B. 55 km C. 65 km D. 75 km

When the truck meets six buses on the way, the driving time of the truck is t = 15min × 5 = 75min = 1.25h; when it meets seven buses, the driving time is 15min × 6 = 90min = 1.5h; so the distance between the two places is s = VT = 40km / h × 1.25h = 50km; when it meets seven buses, the walking distance is S1 = 40km / h × 1.5h = 60km; when it drives forward, it arrives at station B, but it doesn't meet the bus again, so it's necessary The distance between the two places is between 50km and 60km