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14 April, 03:01

Elena and her husband Marc both drive to work. Elena's car has a current mileage (total distance driven) of 15,000 and she drives 15,000 miles more each year. Marc's car has a current mileage of 24,000 and he drives 11,000 miles more each year. Will the mileages for the two cars ever be equal? Explain

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  1. 14 April, 06:36
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    Let us set up a system of functions to describe the given situation and see if they ever intersect.

    Elena has initially 15000 miles and adds 15000 per year.

    we can describe it as Elena = 15000+15000 (years).

    Marc's equation can be given as = 24000+11000 (years).

    Setting both conditions equal, we get

    15000+15000 (years) = 24000+11000 (years).

    Clubbing years on one side we get,

    4000 (years) = 9000

    Lets divide by 4000 on each side we get years = 2.25

    Hence yes, the mileages will equal the same value (whatever it may be) in 2.25 years from the the beginning of the problem.
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