Change the scenario in #3 to be a proportional scenario
To change the scenario in #3 to be a proportional scenario, we need to adjust the values so that they are directly proportional to each other. Here is an example:
Original Scenario (Non-proportional):
Three workers can build a house in 4 weeks.
Proportional Scenario:
Six workers can build the same house in 2 weeks.
Explanation:
In the original non-proportional scenario, the ratio of workers to time was 3:4. To make it proportional, we need to maintain this ratio.
If three workers can build a house in 4 weeks, it means that the number of workers is inversely proportional to the time taken. In other words, if we increase the number of workers, the time taken will decrease proportionally.
In the proportional scenario, we doubled the number of workers from 3 to 6. Therefore, the time taken to build the house should also be halved from 4 weeks to 2 weeks for the ratio to remain the same.
So, in the proportional scenario, six workers can build the same house in 2 weeks.
To change the scenario in question #3 to a proportional scenario, we need to consider a situation where the relationship between the two quantities remains constant.
Original Scenario in question #3:
"An airplane travels 500 miles in 2 hours. How far can it travel in 5 hours?"
For a proportional scenario, we need to look for a pattern where the ratio between the two quantities remains consistent. In this case, since we have a fixed ratio between distance and time, we can change the time in the same proportion to determine the new distance.
Proportional Scenario:
Let's establish the original ratio:
The plane traveled 500 miles in 2 hours, so the ratio of distance to time is 500:2.
To find out how far the plane can travel in 5 hours, we need to scale up this ratio proportionally.
Since the ratio is 500:2, we can divide both sides of the ratio by 2 to simplify it to 250:1. This means that for every 1 hour, the airplane travels 250 miles.
Now, we can multiply this ratio by the new time of 5 hours:
250 miles/hour * 5 hours = 1250 miles
Therefore, in 5 hours, the airplane can travel 1250 miles in the proportional scenario.