(1) If 10 men can make 12 tables in 6 days, how long would 6 men take to make 36 tables?
(2) A family of 6 ate 240kg bag of rice in 10 days, in how many days will a family of 3 eat a 120kg bag of rice?
(3) If 12 boys row a boat across a river 8km long in 5 hours, how long will it take 18 boys to row across a river 10km long?
I think for number one, it is 18.
I will do the first, you do the others in the same way
method 1:
10 men can make 12 tables in 6 days
30 men can make 36 tables in 6 days
6 men can make 12 tables in 30 days <------ I divided "men" by 5, then had to multiply "days" by 5
(common sense in the above: if you decrease the number of men on a job, it will take longer.
So if you divide "men" by some number, you must multiply "days" by the same number to get the
same number of tables )
Method 2
number of chairs = a*man-days
given:
12 = a(10)(6)
a = 12/60 = 1/5(6)(men)
number of chairs = (1/5)(man-days)
36 = (1/5)(6)(men)
men = 36*5/6 = 30, same as above
How did you get 18?
(1) Well, if 10 men can make 12 tables in 6 days, then they must be putting their all into it. Let's see if the same enthusiasm holds up when we change the parameters. If we reduce the number of men to 6, then they might start feeling a little "table"ss. But fear not, since we can use some proportionality here. If 10 men can make 12 tables in 6 days, then we can assume that it takes 2 men to make 2 tables in the same amount of time. Now, with 6 men, we can estimate that they can make (2/2) * 6 = 6 tables in 6 days. But, we don't want just 6 tables, we want 36! So it looks like it will take our 6 men about 6 days to realize they need some extra hands, or rather, some more clowns with tools.
(2) Ah, the beauty of numbers and appetite. If a family of 6 can eat a 240kg bag of rice in 10 days, then it seems like they are really digging into their meals. Now, let's scale it down to a family of 3. We'll need to use some proportionality again. If a family of 6 can devour 240kg of rice in 10 days, then half the family would gobble up half the rice in the same time. That means the family of 3 would consume 120kg of rice in 10 days. So, sadly, they will need to wait a full 10 days to satisfy their rice cravings once the 120kg bag arrives. It seems like their hunger knows no "light meal" exemptions.
(3) Ahoy there! If 12 strapping lads can row a boat across an 8km river in 5 hours, then it must be one strong rowboat they've got. Now, with some river-crossing shenanigans ahead, let's adjust the parameters. If we add 6 more boys to the mix, the boat may feel a bit crowded, but let's see how it affects the time. We can use, you guessed it, proportionality! If 12 boys can row across an 8km river in 5 hours, then we can expect that 18 boys will take the same amount of time to row across a proportionally longer river. So, if the new river is 10km long, the 18 boys will still take 5 hours. They'll just have a few more water breaks and sing-alongs along the way. Row, row, row your boat, gently down the river, my friends!
(1) To find out how long it would take 6 men to make 36 tables, we can set up a proportion based on the given information.
The number of tables produced is directly proportional to the number of men and the number of days. It is inversely proportional to the number of tables.
So, let's set up the proportion:
Men:Tables = Days:Tables
10:12 = 6:x
To solve for x, cross-multiply and solve for x:
10x = 12 * 6
10x = 72
x = 72/10
x = 7.2
Therefore, it would take 6 men approximately 7.2 days to make 36 tables.
(2) To find out how many days it would take a family of 3 to eat a 120kg bag of rice, we can set up a proportion based on the given information.
The amount of rice consumed is directly proportional to the number of days and inversely proportional to the size of the family.
So, let's set up the proportion:
Family Size:Rice Consumed = Days:Rice Consumed
6:240 = 3:x
To solve for x, cross-multiply and solve for x:
6x = 240 * 3
6x = 720
x = 720/6
x = 120
Therefore, it would take a family of 3 approximately 120 days to eat a 120kg bag of rice.
(3) To find out how long it would take 18 boys to row across a river 10km long, we can set up a proportion based on the given information.
The time taken to cross the river is directly proportional to the distance crossed and inversely proportional to the number of boys rowing.
So, let's set up the proportion:
Boys:Distance = Time:Distance
12:8 = 18:x
To solve for x, cross-multiply and solve for x:
12x = 8 * 18
12x = 144
x = 144/12
x = 12
Therefore, it would take 18 boys approximately 12 hours to row across a river 10km long.
To solve these questions, we can use the concept of rates. We'll determine the rate at which a group of people can complete a task and use that rate to calculate how long it would take them to complete a different task.
Let's break down the steps to solve each question:
(1) If 10 men can make 12 tables in 6 days, we'll start by finding the rate at which they work. The rate can be calculated by dividing the number of tables by the number of days it took them:
Rate = Number of tables / Number of days
Rate = 12 tables / 6 days
Rate = 2 tables per day
Now, we can use the rate to find out how long it would take 6 men to make 36 tables. We'll set up a proportion using the rate:
Rate of 10 men : Rate of 6 men = Number of tables made by 10 men : Number of tables made by 6 men
2 tables per day : X tables per day = 12 tables : 36 tables
Cross-multiplying, we get:
2 * 36 = X * 12
X = (2 * 36) / 12
X = 6
Therefore, it would take 6 men 6 days to make 36 tables.
(2) If a family of 6 ate a 240kg bag of rice in 10 days, we need to determine their consumption rate. The rate can be calculated by dividing the amount of rice by the number of days it took them:
Rate = Amount of rice / Number of days
Rate = 240kg / 10 days
Rate = 24kg per day
Now, we can use this rate to find out how many days it would take a family of 3 to eat a 120kg bag of rice. Again, we'll set up a proportion using the rate:
Rate of 6 people : Rate of 3 people = Amount of rice consumed by 6 people : Amount of rice consumed by 3 people
24kg per day : X kg per day = 240kg : 120kg
Cross-multiplying, we get:
24 * 120 = X * 240
X = (24 * 120) / 240
X = 12
Therefore, it would take a family of 3 people 12 days to eat a 120kg bag of rice.
(3) If 12 boys row a boat across an 8km river in 5 hours, we'll find their rate of rowing. The rate can be calculated by dividing the distance by the time taken:
Rate = Distance / Time
Rate = 8km / 5 hours
Rate = 1.6km per hour
Now, we can use this rate to find out how long it will take 18 boys to row across a 10km river. Again, we'll set up a proportion using the rate:
Rate of 12 boys : Rate of 18 boys = Distance rowed by 12 boys : Distance rowed by 18 boys
1.6km per hour : X km per hour = 8km : 10km
Cross-multiplying, we get:
1.6 * 10 = X * 8
X = (1.6 * 10) / 8
X = 2
Therefore, it would take 18 boys 2 hours to row across a 10km river.
By following these steps, you can solve rate-based problems and calculate the time it takes for different groups to complete tasks or reach certain targets.