Solution: Let A run X laps per minute and B run Y laps per minute.
2(x+y)= 1
6(x-y)= 1
Solution:
x= 1/3
y= 1/6
A: A runs 1/3 laps per minute, and B runs 1/6 laps per minute.
2. One A-shaped steel plate can be made into two C-shaped steel plates and 1 D-shaped steel plates; A B-type steel plate can be made into 1 fast C-type steel plate and 2-fast D-type steel plate. Now we need 15 fast C-type steel plate and 18 D-type steel plate. How much steel plate A and B can be used?
Solution: let type A use X sheets and type B use Y sheets.
2x+y= 15
x+2y= 18
Solution:
x=4
y=7
A: Four for Type A and seven for Type B..
3: There are two kinds of bowls for holding wine. It is known that 5 barrels plus 1 keg can hold 3 pots of wine, and 1 keg plus 5 kegs can hold 2 pots of wine. 1 How many pots can a vat hold and a barrel hold?
Solution: 1 Big barrel can hold X pots of wine, 1 Small barrel can hold Y pots of wine.
5x+y=3
x+5y=2
Solution:
x= 13/24
y=7/24
A: The vat can hold 13/24 pots of wine, and the keg can hold 7/24 pots of wine.
4: Take a spring, when it hangs a 2kg object, its length is16.4 cm; ; Hang a 5kg object with a length of 17.9cm. How long should the spring be?
Solution: let the original length of the spring be x cm, and the length can be increased by y cm for every kilogram of weight.
x+2y= 16.4
x+5y= 17.9
Solution:
x= 15.4
y=0.5
Answer: The spring should be15.4cm..
5: There were 1, 5, 1 yuan 10 coins, of which 15 coins were taken out. How many * * * coins do you take from 7 yuan, 1 and 55438+0 yuan?
Solution: 1 angle takes X, 5 angle takes Y, 1 element takes Z; X, Y, z y and Z are integers, and they are all greater than or equal to 0 and less than or equal to 10.
x+y+z= 15
x+5y+ 10z=70
If you want to reduce these two types, you must:
4y+9z=55
y=(55-9z)/4
When z=3, y has a positive integer solution, y=7,
At this point, x= 15-3-7=5.
Answer: 1 corner takes 5 pieces, 5 corners takes 7 pieces and 1 yuan takes 3 pieces.
6. The whole journey from A to B is 3.3km, including uphill section, flat section and downhill section. If the uphill journey is 3 kilometers per hour, the flat road is 4 kilometers per hour, and the downhill journey is 5 kilometers per hour, then it takes 5 1 minute from A to B and 53.4 minutes from B to A. What is the format of the uphill, flat road and downhill journey from A to B?
Solution: suppose from a to b, it is x kilometers uphill, y kilometers flat slope and z kilometers downhill.
x+y+z=3.3……………………( 1)
x/3+y/4+z/5=5 1/60…………(2)
x/5+y/4+z/3=53.4/60…………(3)
By sorting out (2) and (3), we can get:
20x+ 15y+ 12z = 5 1……………………(4)
12x+ 15y+20z = 53.4…………(5)
(5)-(4), obtaining:
8(z-x)=2.4
z-x=0.3
z=x+0.3…………(6)
(6) Substituting (1), we get:
x+y+x+0.3=3.3
2x+y=3
y = 3-2x ……( 7)
Substituting (6) and (7) into (4) gives:
20x+ 15(3-2x)+ 12(x+0.3)= 5 1
20x+45-30x+ 12x+3.6 = 5 1
2x=2.4
x= 1.2
Substitute (6) and (7) respectively to obtain:
y=3-2× 1.2=0.6
z= 1.2+0.3= 1.5
Answer: From A to B, uphill 1.2km, flat slope 0.6km, downhill 1.5km.
7. It takes 10 hour for a ship to sail from A in the upper reaches of a river to B in the lower reaches, and it takes less than 12 hours to return from B at a constant speed. The speed of this river is 3 kilometers per hour, and the still water speed V of the ship's return remains unchanged. What conditions does v meet?
Answer: According to the meaning of the question, you must:
12(v-3)> 10(v+3)
12v-36 & gt； 10v+30
2v & gt66
v & gt33
8. Lao Zhang and Lao Li bought the same number of breeding rabbits. One year later, the number of rabbits bred by Lao Zhang increased by 2, and that of Lao Li decreased by 1 rabbit, and the number of rabbits bred by Lao Zhang did not exceed 2/3 of that of Lao Li. How many kinds of rabbits did Lao Zhang buy at least a year ago?
Solution: Suppose Lao Zhang bought at least X rabbits a year ago, and X is a positive integer.
x+2≤2/3(2x- 1)
3(x+2)≤2(2x- 1)
3x+6≤4x-2
x≥8
A year ago, Lao Zhang bought at least eight rabbits.
9. In the school volleyball league, four classes in the same group played a single round robin match, and the last class was eliminated. If the last few lessons are equal, there will be play-offs between them. Grade 7 1 class can win at least one round of round robin. Can this class be guaranteed not to be eliminated before the play-off? Are you sure to qualify? Why?
Solution:
Single-cycle competition,
There are three games in each class.
One * * * to be played: 4×3÷2=6 games.
Class 7 (1) won at least 1 game.
If this level is eliminated before the final
Then there are three classes left, and each class must win at least two games.
There must be at least 2×3+ 1=7 victories.
It exceeds the total number of competitions, so this class will not be eliminated before the play-offs.
If there are three teams left, one team won all three games.
One ***6 games, 3 victories left.
Then all three classes including Class 7 (1) may only win 1 game.
You need to play a play-off, so you can't guarantee qualifying.