The first autumn of mathematics

1. A middle school organized an autumn outing for grade seven students. It was originally planned to rent bus No.45, but 15 people had no seats. If you rent the same number of 60-seat buses and have one more, the rest will be just full. It is understood that each of the 45-seat buses rents 220 yuan, and each of the 60-seat buses rents 300 yuan.

(1) How many students are there in Grade 7?

Solution: If there are X people in a car, there are (45x+ 15) people.

According to the meaning of the question:

45x+ 15=60x-60

- 15x=-75

x=5

45x+ 15=240

A: There are 240 seventh-grade students.

2) How to rent a car more reasonably so that every student can have a seat? What's the minimum rent?

Solution: Set up x shopping carts.

According to ~ ~ ~

60x=240

x=4

4*300= 1200 (yuan)

Answer: Use 4 trolleys, and the rent is 1200 yuan.

2. A local train goes from A to B. Three hours after departure, an express train also goes from A to B. The express train arrives in BD 45 minutes earlier than the local train, with a full speed of 40km/h.. The express train is twice as fast as the local train. Find the distance between a and b.

Solution: let x kilometers between a and b.

According to ~ ~ ~

X/40=x/(2*40)+3+0.75(45 minutes)

x/40=x/80+3.75

2x=x+300

x=300

A: it's 300km between a and B.

3. The seventh-grade students in a school arrive 3 kilometers away from the school at a speed of 80 meters per minute. When Xiao Ming got to school, the students had already left 10 minutes, so Xiao Ming chased everyone at a speed of 240 meters per minute and caught up on the road.

(1) How long did it take Xiao Ming to catch up with everyone?

Answer: it takes x minutes.

According to ~ ~ ~

240x-80x= 10*80

160x=800

x=5

A: It took five minutes.

(2) How far is it from the scenic spot when catching up with everyone?

Solution 3 km = 3000 m

=3000-5*240

=3000- 1200

= 1800 (m)

A: There is still 1800 meters. ..

3. A rides a bike from place A to place B, and B rides a bike from place B to place A. A walks 2 kilometers more than B every hour. Both of them leave at 8: 00 in the morning, and 10 is still 36 kilometers apart in the morning and 12 is 36 kilometers apart at noon. Find the distance between a and b.

Solution: let A x km/h, then b (x-2) km/h.

According to ~ ~

36-(-36)/( 10-8)

=72/2

=36 km

x+(x-2)=36

x+x-2=36

2x=38

x= 19

x-2= 17

( 10-8)*( 19+ 17)+36

=2*36+36