Hello friends’ Previously we have discussed about longhand subtraction and today we are going to discuss a very interesting topic Rate and Work which is included in grade IX of Maharashtra Board Syllabus and In my opinion it can play a vital role in your Homework help, friends rate and work problems involve the calculations of time in which a work can be done, by a single person or machine or together by a group of two or more people or machines, friends’ rate represents the capacity of a person or machine of doing work with respect to time, friends’ the method of solving work and rate problems is not obvious, there is a trick to solve the rate and work problems, and the trick is we have to think of the problem of how much work each person or machine does in each unit of time, rate and work problems can better be understood by taking some examples:
Example. Suppose a painter can paint a entire house in 12 hours, and the second painter takes 8 hours to paint it, how long will it take the two painters to paint the entire house together,
Friends’ here we can proceed in the following way, as first painter can paint the house in 12 hours,
So here first of all we will find his rate of doing work which can be find out by dividing 1 by 12,
Here it means that the first painter can do 1/12th part of the job per hour similarly for the second painter, we can find his rate of doing work by dividing 1/8, here it means that second painter can do 1/8th part of the job per hour, now to find out how much can they do if they work together, to find this we have to add their individual rate of doing work
So adding their rates we obtain 1/12 + 1/8 = 5/24 which means that if they work together than they can do 5/24 of the job together per hour.
Now let’s say‘t’ is the time taken to complete the job if they work together,
So work completed per hour will be equal to 1/t which is also equal to 5/24 as we have calculated above, now equating to expressions we obtain 1/t = 5/24, or
t = 24/5 =4.8 hours
Now we can say that they will take 4.8 hours to complete the job if they work together,
Example: one pipe can fill a pool 1.25 times faster than a second pipe, when both the pipes are opened they fill the pool in five hours. How long will it take to fill the pool if only the slower pipe is used?
Now again we proceed in the same we lets say faster pipe can fill the pool in t hours, that is why slower pipe will fill the pool in 1.25t hours,
Now converting in their rate form faster pipe can do 1/t job per hour and slower pipe can do 1/1.25t job per hour and together they can do 1/t + 1/1.25t job per hour which should be equal to 1/5
Now equating the two expressions we obtain 1/t + 1/1.25t = 1/5 or
5 + 5/1.25 = f or f = 5+ 4 = 9
Hence faster pipe will take 9 hours to fill the pool and the slower pipe will take
1.25f = 1.25×9 = 11.25 hours to fill the job.
This is all about the problem based on Rate and if anyone want to know about Isosceles triangle theorem then they can refer to internet and text books for understanding it more precisely.Read more maths topics of different grades such as symmetry in the next session here.
Example. Suppose a painter can paint a entire house in 12 hours, and the second painter takes 8 hours to paint it, how long will it take the two painters to paint the entire house together,
Friends’ here we can proceed in the following way, as first painter can paint the house in 12 hours,
So here first of all we will find his rate of doing work which can be find out by dividing 1 by 12,
Here it means that the first painter can do 1/12th part of the job per hour similarly for the second painter, we can find his rate of doing work by dividing 1/8, here it means that second painter can do 1/8th part of the job per hour, now to find out how much can they do if they work together, to find this we have to add their individual rate of doing work
So adding their rates we obtain 1/12 + 1/8 = 5/24 which means that if they work together than they can do 5/24 of the job together per hour.
Now let’s say‘t’ is the time taken to complete the job if they work together,
So work completed per hour will be equal to 1/t which is also equal to 5/24 as we have calculated above, now equating to expressions we obtain 1/t = 5/24, or
t = 24/5 =4.8 hours
Now we can say that they will take 4.8 hours to complete the job if they work together,
Example: one pipe can fill a pool 1.25 times faster than a second pipe, when both the pipes are opened they fill the pool in five hours. How long will it take to fill the pool if only the slower pipe is used?
Now again we proceed in the same we lets say faster pipe can fill the pool in t hours, that is why slower pipe will fill the pool in 1.25t hours,
Now converting in their rate form faster pipe can do 1/t job per hour and slower pipe can do 1/1.25t job per hour and together they can do 1/t + 1/1.25t job per hour which should be equal to 1/5
Now equating the two expressions we obtain 1/t + 1/1.25t = 1/5 or
5 + 5/1.25 = f or f = 5+ 4 = 9
Hence faster pipe will take 9 hours to fill the pool and the slower pipe will take
1.25f = 1.25×9 = 11.25 hours to fill the job.
This is all about the problem based on Rate and if anyone want to know about Isosceles triangle theorem then they can refer to internet and text books for understanding it more precisely.Read more maths topics of different grades such as symmetry in the next session here.
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