Solution: Let's assume that the original speeds of Party A and Party B are A km and B km per day respectively.
According to the meaning of the question
(a+b)×50=200( 1)
10×(a+0.6)+40a+30b+ 10×(b+0.4)= 200(2)
simplify
a+b=4(3)
a+0.6+4a+3b+b+0.4=20
5a+4b= 19(4)
(4)-(3)×4
A =19-4× 4 = 3km.
B = 4-3 = 1 km
A repairs 3 kilometers every day, and B repairs 1 kilometer every day.
A It was originally planned to build 3× 50 = 150km.
B 1× 50 = 50km as originally planned.
2. Xiaohua bought four mechanical pencil and two pens, and paid 14 yuan; Xiaolan bought the same 1 mechanical pencil and two pens, and paid 1 1 yuan. Find the unit price of mechanical pencil and pen.
Solution: Suppose mechanical pencil has a pen with X yuan and a pen with Y yuan.
4X+2Y= 14
X+2Y= 1 1
The solution is X= 1.
Y=5
In mechanical pencil, the unit price is 1 yuan.
Pen unit price 5 yuan
1. The distance between the two stations is 275 kilometers. The local train goes from Station A to bilibili at a speed of 50 kilometers per hour. 1h later, the express train runs from bilibili to Station A at a speed of 75km/ h. How many hours after the local train leaves, will you meet the express train?
Set the local train to meet the express train in an hour.
50a+75(a- 1)=275
50a+75a-75=275
125a=350
A=2.8 hours
2. A car travels from place A to place B at a speed of 40 kilometers per hour. After 3 hours, due to the rain, the average speed was forced to drop 10km. The result arrived at B 45 minutes later than expected. Find the distance between a and b.
Set the original time to one hour.
45 minutes =3/4 hours
According to the meaning of the question
40a = 40×3+(40- 10)×(a-3+3/4)
40a= 120+30a-67.5
10a=52.5
A=5.25=5, 1/4 hours =2 1/4 hours.
So the distance between Party A and Party B is 40×2 1/4=2 10 km.
The locksmith class in a workshop is divided into two teams to watch the tree planting work. The number of people in Team A is twice that of Team B. If 16 people are transferred from Team A to Team B, the number of people left in Team A is three less than that of Team B. What about the original numbers of Team A and Team B?
Solution: Team B originally had A, while Team A had 2a.
Then according to the meaning of the question
2a- 16 = 1/2×(a+ 16)-3
4a-32=a+ 16-6
3a=42
a= 14
Then team B was originally 14, and team A was originally 14×2=28.
At present, team B 14+ 16=30 people, and team A = 28- 16= 12 people.
4. It is known that the profit of a store in March is 654.38+10,000 yuan, and the profit in May is1320,000 yuan. The month-on-month growth rate in May was 654.38+00 percentage points higher than that in April. Find the monthly growth rate in March.
Solution: Let April profit be X.
Then x * (1+10%) =13.2.
So x= 12.
Let the growth rate in March be y.
Then10 * (1+y) = X.
y=0.2=20%
So the growth rate in March was 20%
A motorcycle and a truck are driving from place A to place B at the same time. When the motorcycle has traveled 1/3 of the whole journey, the truck is still 1 14 kilometers away from B. At this speed, when the motorcycle arrives at B, the truck has already traveled five-eighths of the whole journey. How many kilometers is it between A and B?
Solution: Speed ratio of motorcycle and truck = distance ratio = 1: 5/8 = 8: 5.
So when the motorcycle travels 1/3, the truck travels 1/3×5/8=5/24.
Then the distance between Party A and Party B =114/(1-5/24) =114/(19/24) =144km.
75. It takes 8 minutes to walk from A, and Xiao Qiang from B. Is Xiaoming still110 from B, and Xiao Qiang is 15 meters from A, which shows that Xiaoming walks 5 meters less than Xiao Qiang every minute. How many meters is there between AB and B?
Solution: Xiaoming walks 5× 8 = 40m less than Xiao Qiang.
AB distance = (40+15)/(110) = 550m.
76. Party A and Party B set out from Town A at the same time and went to Town B, which is 90 kilometers away. Party A rides a bike at 30km per hour, and Party B walks at 10km per hour. It took Party A 1 hour to return to Town B and met Party B on the way. B how many kilometers did you walk at this time?
Solution: It takes 90/30 = 3 hours from A to B town.
It takes 1 hour to do something again, so at this time, B has 3+ 1=4 hours left.
Distance =10× 4 = 40km
At this time, the distance between Party A and Party B is 90-40 = 50km.
Meeting time =50/(30+ 10)=5/4 hours.
Then B walked 40+ 10×5/4=52.5 kilometers.
77. Buses and trucks run in opposite directions from the midpoint of Party A and Party B at the same time. Five hours later, the bus arrives at Party B, and the truck is 60 kilometers away from Party B. Given the speed ratio of the truck to the bus is 5:7, how many kilometers are the two places apart?
Solution: In the same time, speed ratio = distance ratio.
Then the distance ratio between trucks and buses is 5: 7.
The bus traveled all the way 1/2.
Then the truck has traveled all the way (1/2)×5/7=5/ 14.
Then the whole journey = 60/(1/2+5/14) = 60/(12/14) = 70km.