50(X+8)=60(X-5)
X=70
50(X+8)=50*78=3900 meters The distance from the students' home to the school is 3900 meters.
A project needs to be completed within the specified time. If 6 people are reduced, the working hours will be increased 12 days; If the number of workers increases by four, the working hours will be reduced by four days. Try to find the stipulated time and the original number of people? (solved by binary linear equation)
X people, y days:
XY =(X-6)(Y+ 12)= XY-6Y+ 12X-72
XY =(X+4)(Y-4)= XY+4Y-4X- 16
X= 16 people
Y=20 days
Party A and Party B set out from Party A and Party B at the same time, and the first meeting was more than 50 meters away from the midpoint. After Party A and Party B arrive at Party B, they immediately turn around and go back. So, Party A and Party B met for the second time at a distance of 0/00 meters from Party A/KLOC-to find out the distance between Party A and Party B. ..
Let the distance between Party A and Party B be X, and when they meet for the second time, the distance they walked is three times that of the first time. A:
(2X- 100)/3=X/2+50
X=500 meters
4 A and B walk in opposite directions at the same time from A and B respectively. The first encounter was at a distance of 100 km. After the encounter, the two cars continued to drive at the original speed. After reaching the starting point on the other side, they return at the original speed. The second meeting, 30 kilometers away from point A in AB. Find the distance between a and b.
The distance between A and B is S, so when they meet for the first time, two cars * * * take S, and when they meet for the second time, two cars * * * take 3S.
A car: 3* 100= 1.5S+30.
S= 180
The distance between a and b is 180km.
5. Two cars, A and B, start from the East and West Stations at the same time, heading in opposite directions. After they met, they went forward at the original speed, returned immediately after reaching the starting point of each other, and met again on the way. It is known that the speed of car A is 40 kilometers per hour, 8 kilometers more than that of car B, and the distance between the two meeting places is 80 kilometers. Find out the distance between the east and west stations.
Suppose we meet for the first time at t, then the distance between east and west stations is (40+32)t=72t.
The time from the first meeting to the second meeting is 2t.
80t-64t=80 t=5 (hours)
(40+32)t=360 km
6 Party A, Party B and Party C process a batch of parts, Party A completes 2/5 of all parts, Party C processes 5/7 of the parts processed by Party B, and Party C produces 36 parts less than Party B. How many parts do they produce respectively?
Let the total number be X and B be Y, then A is 2X/5 and C is 5Y/7:
Y-5Y/7 = 36Y = 126B
5Y/7=90 degrees Celsius
2X/5+ 126+90=X X=360
360- 126-90 = 144A
Xiaoxiao's faucet is broken and often leaks. Xiaoxiao uses a bucket with a volume of 3 liters to receive water, 1 hour will be full in 30 minutes. If the water fee per cubic meter is 1.8 yuan, how much water is wasted in one month? How many days of wasted water can a person drink a month? (Drink 1400 ml per person per day)
3/ 1.5 = 2L/ hour wastes 2 liters of water per hour.
2 * 24 * 30 *1.81000 = 2.592 yuan a month wasted 2.592 yuan of water.
2 * 24 * 30/1.4 =1028.57 days
A shop bought two baskets of apples, A and B, weighing 200 Jin. If you take out 1 1 from the first basket and put it in the second basket, then the first basket is less than the second basket 165438+2+0. How many kilograms of apples are there in baskets A and B?
x+y=200
10x/ 1 1:(y+x/ 1 1)= 9/ 1 1: 1
99y= 10 1x
X=99 kg A。
Y= 10 1 kg B。
It takes 6 days for Party A, Party B and Party C to cooperate to complete a project. Now Party A and Party B cooperate 1 day, and then Party C works alone for 8 days. What is the function of C?
1/x+ 1/y+ 1/z = 1/6
1/x+ 1/y+8/z = 1
Z=8.4 days
C it takes 8.4 days to do it alone.
10 is equipped with 10 people, and each person carries a bucket and draws water at the same time. It takes 1 minute to fill the bucket of the first person and 2 minutes to fill the bucket of the second person ..... So, when there are only two faucets, 10 people are cleverly arranged to fetch water, so that their total time consumption is the least. This time is () minutes.
1+ 10+3+8+5=27
2+9+4+7+6=28
This time is (28) minutes
1 1 grade 7 1 class, with a book corner. The whole class donated books 188, of which 6 students donated 2 books and the rest donated 4 books. Are there any students in this class?
(188-6*2)/4+6=50 students
12 Several people buy sheep together. If everyone pays 5 yuan, it is not as good as 45 yuan; If everyone pays 7 yuan and he is still short of 3 yuan, then ask the number of sheep to buy and the price of sheep.
Suppose the number of sheep bought is a.
5a+45=7a+3
a=2 1
Sheep price =5*2 1+45= 150.
13 Both cars leave from AB at the same time. They met for the first time in a place 32 kilometers away. After the meeting, the two cars continued to drive. After arriving in Ba, they immediately returned along the original road and met for the second time at a distance of 64 kilometers. How many kilometers is the whole journey from AB to A?
When we meet for the first time, we go in one direction, and when we meet for the second time, we go in two directions. Then the distance traveled by car A from departure to the second encounter is three times that of the first encounter-32 * 3 = 96 kilometers. At this time, the distance between the A train and the starting point is 64 kilometers, and 96+64= 160 kilometers is two one-way.
Then the distance between AB and AB is 160/2 = 80km.
14 Li Ming, Xinhe Wang, two people run in opposite directions around the circular runway at a constant speed, starting from both ends of the diameter. If they start at the same time and meet for the first time when Wang Xin runs 100 meters, and meet for the second time when Wang Xin is 60 meters short, what is the circumference of the runway?
3* 100=x-60
x=360
The circumference is 360 meters.
15 The distance between Party A and Party B is 350km. An express train and a local train leave from two places at the same time and meet in 3.5 hours. As we all know, the speed ratio of the express train to the local train is 3: 2. What's the speed of these two trains?
The distance between the two places is 350 kilometers. They meet after 3.5 hours and walk 350/3.5= 100 kilometers per hour.
The speed ratio between the express train and the local train is 3: 2, so the express train goes 100 * 6/ 10 = 60km, and the local train goes 100 * 4/ 10 = 40km, that is, the express train speed is 60km/h and the local train speed is 40km/.
16 Xiao Zhang's bicycle speed 15 km, Xiao Wang's motorcycle speed is 35 km/h. Both of them started from ab at the same time and drove back and forth continuously in ab. The place where they met for the first time and the place where they met for the second time were exactly 45 kilometers apart. So what's the distance between ab two points?
9X/ 10-3X/ 10=45
X=75
17 There are strange stones every other meter on the straight line. We should concentrate the stones in the middle, starting with the correct stones, and only move one stone at a time in order. If someone moves stones like this, all the stones are concentrated in the middle except the one in the middle, and * * * has already walked 300 meters. How many stones were put in the * *?
Let * * have 2X+ 1 pebble, then move the pebble of the rightmost pebble, walk x meters, follow it to the position of X- 1 on the right, and then walk 2(X- 1) meters to the position between them, and so on, and move all the pebbles on the right:
X+2[(X- 1)+(X-2)+...+2+ 1]=x+2*[(x- 1)+ 1](x- 1)/2=x+x(x- 1)=x^2
It takes x meters to move the stone on the left than to move the stone on the right, but it takes 2X meters to move the stone on the left (it takes x meters to move the stone on the right), so all the stones on the left are moved by x 2+X.
X^2+X^2+X=300
X^2+X/2= 150
X= 12
2X+ 1=25 *** There are 25 stones.
18 Kuai, Zhong and slow three started from the same place at the same time and caught up with the cyclists in front along the same highway. The speed is constant. The three cars caught up with the autobots in 6 minutes, 10 minutes and 12 minutes respectively. Now we know that the speed of the express train is 24 kilometers per hour. The speed of the middle train is 20 kilometers per hour, and how many kilometers per hour is the local train?
When the express train catches up with the cyclist, it separates from the intermediate train;
(24-20) * 6/60 = 0.4km。
That is, the distance between the central train and the cyclist is 0.4 km at this time.
It takes 10-6=4 minutes to catch up with the car.
So the speed of the cyclist is 20-0.4/(4/60) = 14km per hour.
When the three cars left, they separated from the cyclist:
(24- 14)* 6/60 = 1 km
/kloc-catch the local train in 0/2 minutes, and there are more routes per hour than cyclists;
1/(12/60) = 5km
So the local speed is 14+5= 19 km per hour.
19 the passenger ship sailed from port a to port b, and the cargo ship sailed from port b to port a, and the two ships sailed opposite each other, meeting 10 hour, and then continuing to drive for 3 hours. At this time, the passenger ship is 280 kilometers away from Port B, and the cargo ship is 420 kilometers away from Port A. How many kilometers are there between Port A and Port B?
Solution: If the sum of the speeds of passenger ships and cargo ships is A, then the meaning of the question is:
10a = 3a+280+420 Solution: A = 100 So the distance between port A and port B is10×100 =1000 km.
20 A to b is a ramp. The car goes up the hill at 30 kilometers per hour and down the hill at 45 kilometers per hour. It takes three hours to go back and forth. How many kilometers is it between A and B?
Let the distance of 2 be x.
It takes X/30 to climb a mountain.
The downhill time is X/45.
X/30+X/45=3
The solution is X=54.