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Algebra

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I am so lost can someone please help me

Trains A and B are traveling in the same direction on parallel tracks. Train A is traveling at 80 miles per hour and train B is traveling at 100 miles per hour. Train A passes a station at 11:15am. If train B passes the same station at 11:27a.m., at what time will train B catch up with train A?

  • Algebra - ,

    At 11:27, when B is at the station, train A will have traveled 12 minutes at 80 mph for a distance of 80(1/60) or 16 miles

    So draw a line with B at the station on the left, A 16 miles to the right of B.
    Let the distance that A still travels before B catches up be x miles, call that point P

    So AP = x, BP = x+16
    Time for B to reach P is (x+16)/100
    time for A to reach P is x/80

    but those times are equal, so
    (x+16)/100 = x/80
    .
    .
    x = 64

    so time for A to reach P is 64/80 = .8 hrs, or 48 minutes.

    so the time when it happens is 11:27 + 0:48 = 1:15 pm

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