14 A rapid transit system has just started operating In the

14. A rapid transit system has just started operating. In the first month of operation, it was found that 25% of commuters are using the system, while 75% are traveling by automobile. Suppose that each month 10% of transit users go back to using their cars, while 30% of automobile users switch to the transit system. What will be the fractions using rapid transit in the fourth month?

Solution

First month

Transit 1/4

Car 3/4

Second month

Transit : 1/4 - 1/40 + (3/10)(3/4) = 9/20

Car : 3/4 +1/40 - (3/10)(3/4) = 11/20

Third month

Transit: 9/20 - 9/200 + 33/200 = 57/100

Car: 11/20 + 9/200 - 33/200 = 43/100

Fourth month:

Tranist: 57/100 - 57/1000 + 129/1000 = 321/500

Car: 43/100 + 57/1000 - 129/1000 = 179/500