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Mathematical problems of assembling car
1, let big x yuan, weight y, small price =0.8x, weight =3y/2.

y+3y/2= 100

Y=40 Small weight = 60kg

Cost = 5.5 *100/(1+25%) = 440 yuan.

40x+60*0.8x=440

X=5 yuan

Small price =4 yuan.

The mass ratio is 2:3.

Small mass =100/(1+2/3) = 60 kg.

Large size =100-60 = 40kg

Cost = 5.5 *100/(1+25%) = 440 yuan.

40x+60*0.8x=440

X=5 yuan/kg

Small price =4 yuan/kg

2. Solution: Each bicycle is equipped with 2 wheels.

When the rack loader and the wheel loader spend the same time, the number of people is just right.

Three workers assemble 10 frames in 2 hours, which means that 1 frame takes 0.6 man-hours;

Four workers assemble 2 1 wheel in 3 hours, which means that the time consumption of 2 wheels is 24/2 1 man-hour;

The working time ratio is 0.6: 24/21= 0.6 * 21/24 = 21/40.

That is, 2 1 man-hour is used to produce the frame and 40 man-hour is used to produce the wheel.

244 people work 1 hour, and the working time is 244. In proportion, it is used

21* 244/(21+40) = 84 hours to produce the frame, and 160 hours to produce the wheel is just right.

The arrangement is as follows:

84 people, 3 people, 1 group, divided into 28 groups, 1 hour installation 140 aircraft;

160 people, 4 people, 1 group, divided into 40 groups, 1 hour to install 280 wheels.

3. For the first time, if the time is 1/8, the ratio of the original time to the current time is 8: 9, and the ratio of the original speed to the current speed is 9: 8. The original speed is 5 ÷ (1-8/9) = 45km.

The second time, if the speed is 1/3, the ratio of original speed to current speed is 3: 4, and the ratio of original time to current time is 4: 3. The original time is 1÷( 1-3/4)=4 hours.

So we find that the distance between AB and AB is 45×4= 180 km.