Let the average speed be x and the wind speed be y.
[X+Y]*2 .5= 1200
[X-Y]* 10/3= 1200
X=420
Y=60
In other words, the average speed is 420 kilometers per hour. The wind speed is 60 kilometers per hour.
2. An army marched for 4 hours on the first day, 5 hours on the second day, 98 kilometers on the second day, and walked 2 kilometers less on the first day than on the second day. What is the average speed on the first day and the second day?
Let the speed on the first day be x and the speed on the second day be y.
4X+5Y=98
4X+2=5Y
X= 12
Y= 10
That is, the speed on the first day is 12 km/h, and the speed on the second day is10 km/h.
3. There is an uphill road and a flat road from A to B. If you keep going uphill for 3km/h, flat road for 4km/h and downhill for 5km/h, it will take 54 minutes from A to B and 42 minutes from B to A. How much is the whole journey from A to B?
Let's go uphill x kilometers and level the road y kilometers, and then
X/3+Y/4=54/60
X/5+Y/4=42/60
Solve the above equation and get
X= 1.5
Y= 1.6
x+Y = 1.5+ 1.6 = 3. 1
Answer: The whole journey from A to B is 3. 1 km.
These problems can be solved by arithmetic, so as long as there are application problems about equations, there are generally two solutions. For another example, a chicken and a rabbit have 100 feet. If the chicken is replaced by a rabbit and the rabbit is replaced by a chicken, then * * has 88 feet. Q: How many chickens and rabbits are there?
Because chickens are replaced by rabbits and rabbits are replaced by chickens, the number of feet is reduced 100-88 = 12 (only one), while a rabbit is replaced by chicken feet and a chicken is replaced by rabbit feet. The total number of feet decreased, indicating that there were more rabbits than chickens. How much more? In fact, rabbits have more feet than chickens, that is, 100-88 = 12 (only). Because rabbits have two more feet than chickens, a = 12 ÷ 2 = 6 (only). In other words, rabbits have six more feet than chickens. Now the question becomes: "
After chickens were replaced by rabbits, the number of feet decreased.
100-88 = 12 (only),
So there are more rabbits than chickens.
12÷ (4-2) = 6 (only).
These four rabbits are 6× 4 = 24 feet.
Therefore, the equivalent chicken and rabbit feet are 100-24 = 76 (only).
Because a chicken and a rabbit have six feet, the number of chickens is
76÷ 6 = 38/3 (only).
The number of rabbits is 38/3+6 = 56/3 (only).
Equation solution:
Let the chicken be x and the rabbit be y, then there is an equation:
2X+4Y= 100
2Y+4X=88
Solution, X=38/3
Y=56/3
Workers process 6 machines in 1 hour. How many hours does it take to process 72 machines?
Solution 1:72÷6= 12
Solution 2:72÷6=x
x=72÷6
x= 12
1. The flight route from city A to city B is 1200 kilometers long. It takes 2 hours and 30 minutes for the plane to fly downwind from City A and 3 hours and 20 minutes to fly upwind from City B.. What is the average speed and wind speed of the plane?
Let the average speed be x and the wind speed be y.
[X+Y]*2 .5= 1200
[X-Y]* 10/3= 1200
X=420
Y=60
In other words, the average speed is 420 kilometers per hour. The wind speed is 60 kilometers per hour.
2. An army marched for 4 hours on the first day, 5 hours on the second day, 98 kilometers on the second day, and walked 2 kilometers less on the first day than on the second day. What is the average speed on the first day and the second day?
Let the speed on the first day be x and the speed on the second day be y.
4X+5Y=98
4X+2=5Y
X= 12
Y= 10
That is, the speed on the first day is 12 km/h, and the speed on the second day is10 km/h.
3. There is an uphill road and a flat road from A to B. If you keep going uphill for 3km/h, flat road for 4km/h and downhill for 5km/h, it will take 54 minutes from A to B and 42 minutes from B to A. How much is the whole journey from A to B?
Let's go uphill x kilometers and level the road y kilometers, and then
X/3+Y/4=54/60
X/5+Y/4=42/60
Solve the above equation and get
X= 1.5
Y= 1.6
x+Y = 1.5+ 1.6 = 3. 1
Answer: The whole journey from A to B is 3. 1 km.
These problems can be solved by arithmetic, so as long as there are application problems about equations, there are generally two solutions. For another example, a chicken and a rabbit have 100 feet. If the chicken is replaced by a rabbit and the rabbit is replaced by a chicken, then * * has 88 feet. Q: How many chickens and rabbits are there?
Because chickens are replaced by rabbits and rabbits are replaced by chickens, the number of feet is reduced 100-88 = 12 (only one), while a rabbit is replaced by chicken feet and a chicken is replaced by rabbit feet. The total number of feet decreased, indicating that there were more rabbits than chickens. How much more? In fact, rabbits have more feet than chickens, that is, 100-88 = 12 (only). Because rabbits have two more feet than chickens, a = 12 ÷ 2 = 6 (only). In other words, rabbits have six more feet than chickens. Now the question becomes: "
After chickens were replaced by rabbits, the number of feet decreased.
100-88 = 12 (only),
So there are more rabbits than chickens.
12÷ (4-2) = 6 (only).
These four rabbits are 6× 4 = 24 feet.
Therefore, the equivalent chicken and rabbit feet are 100-24 = 76 (only).
Because a chicken and a rabbit have six feet, the number of chickens is
76÷ 6 = 38/3 (only).
The number of rabbits is 38/3+6 = 56/3 (only).
Equation solution:
Let the chicken be x and the rabbit be y, then there is an equation:
2X+4Y= 100
2Y+4X=88
Solution, X=38/3
Y=56/3