Within a large metropolitan area, 20% of the commuters currently use the public transportation system, whereas the remaining 80% commute via automobile. The city has recently revitalized and expanded its public transportation system. It is expected that 6 months from now 40% of those who are now commuting to work via automobile will switch to public transportation, and 60% will continue to commute via automobile. At the same time, it is expected that 20% of those now using public transportation will commute via automobile and 80% will continue to use public transportation.
What percentage of the commuters are expected to use public transportation 6 months from now?

Question

Within a large metropolitan area, 20% of the commuters currently use the public transportation system, whereas the remaining 80% commute via automobile. The city has recently revitalized and expanded its public transportation system. It is expected that 6 months from now 40% of those who are now commuting to work via automobile will switch to public transportation, and 60% will continue to commute via automobile. At the same time, it is expected that 20% of those now using public transportation will commute via automobile and 80% will continue to use public transportation. ​
What percentage of the commuters are expected to use public transportation 6 months from now?
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Quizplus · Accepted Answer

To solve the problem, we can use a table to represent the current and future states of commuting:

|                      | Public Transportation | Automobile | Total   |
|----------------------|-----------------------|------------|---------|
| Now                  | 20%                   | 80%        | 100%   |
| 6 months from now     | 32%                   | 68%        | 100%   |

Starting from the "Now" row, we can fill in the "6 months from now" row by applying the given percentages:

- 40% of automobile commuters will switch to public transportation: 0.4 x 80% = 32%
- 20% of public transportation users will switch to automobile: 0.2 x 20% = 4%
- The remaining percentages can be calculated by subtraction: 100% - 32% - 4% = 64% for automobile, and 100% - 32% = 68% for public transportation.

Therefore, the answer is 48%, which corresponds to the percentage of commuters using public transportation 6 months from now.

Within a Large Metropolitan Area, 20% of the Commuters Currently