The encyclopedia of commonly used mathematical formulas is here!
1, chickens and rabbits in the same cage?
Number of chickens = (number of rabbit feet x total number of heads-total number of feet)/(number of rabbit feet-chicken feet)
Number of rabbits = (total number of feet-chicken feet x total number of heads)/(number of rabbit feet-chicken feet)
2. Tap water problem
Downstream speed = ship speed+water speed, downstream speed = ship speed-water speed?
Upstream speed = (downstream speed+upstream speed) /2?
Upstream speed = (downstream speed-upstream speed) /2?
3. The train problem?
Train speed x time = train length+bridge length?
1) overtaking problem (driving in the same direction, catching up problem)
Distance difference = sum of body length?
Overtaking time = body length and/or speed difference?
2) Wrong car problem (reverse movement, encounter problems)
Sum of distances = sum of body length?
Wrong train time = sum of body length/sum of speed?
3) People passing by (people think of it as a train with a body length of 0)
4. What is the formula for the train to cross the bridge?
(bridge length+conductor)/speed = crossing time
(length+conductor)/travel time = speed?
Speed x crossing time = the sum of the length of the bridge and the car?
5. plant trees?
The problem of planting trees on an unclosed line;
(1) interval number+1= tree number; (planting trees at both ends)
Road length/interval length+1= number of trees?
Number of intervals-1= number of trees
(
2) Tree planting on closed lines:?
Road length/number of intervals = number of trees?
Road length/number of sections = road length/number of trees = length of each section?
Length of each interval x number of intervals = length of each interval x number of trees = road length
(3) How many sections are sawed or cut?
Saw number = number of segments-1?
Number of segments = tens of saws 1
(4) Place flowerpots around the regular polygon:?
A. the situation in every corner:
Total number of pots = (number of sides 1)x number of sides?
Number of sides = total number of pots/number of sides+1?
Number of sides = total number of pots/(number of sides-1)
B.if you don't put it in every corner:
Number of sides x number of sides = total number of pots?
Total number of flowerpots/number of sides = number of sides?
Total pots/sides = sides
6. What's the problem with broken rope?
Fold a rope in half n times, cut m knives from it and cut it into pieces.
(2NxM+ 1) section
7. Age?
Multiple changes in the age of two people.
Years later, age = age difference/multiple difference, one year old?
Age a few years ago = young age-age difference/multiple difference.
8. profit and loss problem?
(ten losses and one profit)/the difference between two issues = the number of shares participating in the issue.
(Gross profit and small profit)/the difference between two distributions = the number of shares participating in the distribution.
(One big loss and one small loss)/the difference between the two distributions = the number of shares participating in the distribution?
9. What is the problem of sum and difference times?
Sum and difference problem formula:
(sum and difference) /2= smaller number
(and ten difference) /2= larger number?
Formula of sum and multiple problem:?
Sum/ (multiple of ten 1)= decimal.
Decimal x multiple = large number?
And a decimal = a large number?
The formula difference of differential multiple problem is:?
And/(multiple-1)= decimal?
Decimal x multiple = large number?
Decimal decimal difference = large number
10, cattle grazing problem?
Set the grazing amount of a Niu Yi day as "1".
(1) Growth rate of grass = (corresponding number of bulls x days of eating more-corresponding number of bulls x days of eating less)/(days of eating more-days of eating less)?
(2) The amount of grass = the number of cows' heads x the number of eating days-the growth rate of grass x the number of eating days.
(3) the number of days to eat = the original amount of grass/(the growth rate of a grass is calculated according to the number of cows)
(4) The number of ox heads = the original amount of grass/the number of days to eat+the growth rate of grass?
These four formulas are the basis for solving the problem of growth and decline.
1. (number of cows x days of eating more grass-number of cows x days of eating less grass)/(number of days of eating more grass-days of eating less) = amount of new grass growing in grassland every day?
2. Number of cows x grazing days-new growth per day x grazing days = original grassland grass.