Welcome, young mathematicians, to an exciting journey into the world of proportions! Today, we'll dive into the fantastic realm of indirect. Think about Indirect or inverse proportion as a relation between two quantities where an increase in one leads to a decrease in the other, and vice-versa.
Get
ready to explore these mathematical adventures and discover how these
relationships are all around us. So, grab your math tools and let's embark on a
proportion-filled learning adventure together!
- Consider
a task that needs to be completed, such as painting a wall. The more
workers you assign to the job, the less time it will take to finish. Conversely,
if you reduce the number of workers, the time it takes to complete the
task increases. Here, the number of workers and the time to complete the
task are in an indirect proportion.
In a construction company, a supervisor claims that 5 men can
complete a task in 30 days. In how many days will 10 men finish the same task?
The
answer to this type of problem we need to apply the concept of Inverse
Proportion
But
what is an Inverse Proportion?
- When
an increase in one quantiy causes the decrease of the
other quantity.
- When
the decrease in one quantity causes an increase of the
other quantity.
Inverse
means opposite - what happens in one quantity affect the other
quantity in the opposite way. This is the ooposite of Direct Proportion where
when on quantity increases the other increse or if it decreases so does thr
other.
Lets look at the problem - 5 men can complete a task in 30 days. In how many days will 10 men finish the same task?
If
5 men can do the work in 10 days what do you think will happen if 10 men do the
job. Will it take more or less men? It will take less time of course.
Solution:-
1. The number of workers is inversely proportional to the time need to finish the job
2. The more men work together, the faster the work will be done.
3. The lesser men work together, the slower the work will be done.
Solution:
|
MEN |
TIME
(days) |
|
5 |
30 |
|
10 |
15 |
Multiply the quanties on the same row:
5 x 30
= 10 x N
150
= 10N
150/10
= N
15
= N
Answer: It will take 15 days for 10 men to finish the same job.
2. Travel Time and Speed: Think about a car trip. If you maintain a constant speed, the time it takes to reach your destination will be inversely proportional to your speed. If you drive faster, you'll cover more distance in less time. On the other hand, if you slow down, it will take more time to cover the same distance. So, in this case, travel time and speed are in an indirect proportion.
The time taken by a vehicle is 3 hours at a speed of 60 miles/hour. What would be the speed taken to cover the same distance at 4 hours?
|
SPEED (mph) |
TIME
(hrs) |
|
60 |
3 |
|
45 |
4 |
Solution:
Multiply the quantities in the same line
60 x 3 = N x 4
180 = 4N
180/4 = N
45 = N
Answer. One will have to drive at 45mph to take 4 hours to complete the trip.
Try this example: 20 men can pave a stretch of road in 15 days. How many days will 30 men take to do this same job?
Hint: Start with your table
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Look out for the quiz on Friday!
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