Inverse proportion
4 people clean a sports hall in 30 minutes. If 6 people work, they will take less time, but not by as much as you might guess by eye. The more taps you open to fill a tank, the fewer hours it takes. In these problems, when you multiply one quantity by a number, the other is divided. This is inverse proportion.
What is inverse proportion?
State with reasons whether the following pairs of quantities have an inversely proportional relationship: a) The number of people painting a fence and the time taken to…
State with reasons whether the following pairs of quantities have an inversely proportional relationship:
- a) The number of people painting a fence and the time taken to finish it.
- b) The number of kilograms of apples you buy and the total price you pay.
- c) The speed at which a train travels and the time taken to cover the distance between two cities.
- d) The number of pages in a book and its weight.
To set up the stage for a music festival, $4$ workers worked for $12$ hours. If the festival decides to hire a total of $8$ workers working at the same rate, how many…
To set up the stage for a music festival, $4$ workers worked for $12$ hours. If the festival decides to hire a total of $8$ workers working at the same rate, how many hours will they take to set up the same stage?
The constant product
A group of friends wants to hire a van to go on a trip. If $6$ friends go, each must pay $15$ euros. Calculate how much each would have to pay if $10$ people end up…
A group of friends wants to hire a van to go on a trip. If $6$ friends go, each must pay $15$ euros. Calculate how much each would have to pay if $10$ people end up going on the trip.
To set up the stage for a music festival, $8$ workers worked for $15$ hours. If the local council needs the setup to be finished in just $10$ hours, how many additional…
To set up the stage for a music festival, $8$ workers worked for $15$ hours. If the local council needs the setup to be finished in just $10$ hours, how many additional workers will they need to hire, assuming all work at the same rate?
Inverse rule of three
A group of friends has won a $300$ € prize in a robotics contest and they have decided to share it equally. Complete the following table to find out how much money each…
A group of friends has won a $300$ € prize in a robotics contest and they have decided to share it equally. Complete the following table to find out how much money each one would receive depending on the number of people in the group. Also state what the constant of inverse proportionality is.
| Number of friends ($x$) | $2$ | $3$ | $4$ | $5$ | $6$ |
|---|---|---|---|---|---|
| Money per person ($y$) | $150$ | ? | ? | ? | ? |
In the graph you can see the case of $2$ friends marked.
Two gear wheels are meshed together. The first has $48$ teeth and turns at $150$ revolutions per minute (rpm). At what speed will the second wheel turn if it has $30$…
Two gear wheels are meshed together. The first has $48$ teeth and turns at $150$ revolutions per minute (rpm). At what speed will the second wheel turn if it has $30$ teeth?
Three friends decide to share out the $282$ € prize won in a robotics competition in inverse proportion to the number of minutes they took to solve their final test. If…
Three friends decide to share out the $282$ € prize won in a robotics competition in inverse proportion to the number of minutes they took to solve their final test. If the first friend took $12$ minutes, the second $15$ minutes, and the third $20$ minutes, how much money does each person get?
Back to the start: If 4 people take 30 minutes, the work constant is $4 \cdot 30 = 120\text{ personas}\cdot\text{min}$. With 6 people they will take $120 : 6 = 20\text{ minutes}$.