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 30% of those who are now commuting to work via automobile will switch to public transportation, and 70% will continue to commute via automobile. At the same time, it is expected that 10% of those now using public transportation will commute via automobile and 90% will continue to use public transportation. In the long run, what percentage of the commuters will be using public transportation? (Round your answer to the nearest percent.)

Question

Breean

Mathematics

1 January, 11:06

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 30% of those who are now commuting to work via automobile will switch to public transportation, and 70% will continue to commute via automobile. At the same time, it is expected that 10% of those now using public transportation will commute via automobile and 90% will continue to use public transportation. In the long run, what percentage of the commuters will be using public transportation? (Round your answer to the nearest percent.)

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Answers (1)

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German Oconnell · Answer 1

42%

Step-by-step explanation:

Let's say there are 100 people in the city

Today, 20 use public transport and 80 use their own automobiles

6 months from now, 30% of those using their own car will switch to public transport = 30% x 80 = 24

10% of those using public transport will switch to their own car = 10% x 20 = 2

Therefore, in the future, 20 + 24 - 2 people will use public transport = 42

The answer is therefore 42%