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

Mathematics

Thalia Fischer

4 June, 06:43

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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Daisy Bray · 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%