two joggers used a 2 km circular road for their training. if they start together from the same place and jog in opposite directions, they meet after 15 minutes. However, if they jog in the same direction at the end of one hour and 15 minutes, the faster jogger would have gone 1 1/4 laps farther. How fast did each jog?

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  1. rate of faster --- x km/h
    rate of slower --- y km/h

    going in opposite direction:
    distance covered by slower = (1/4)y
    distance covered by faster = (1/4)x

    (1/4)x + (1/4)y = 2
    x + y = 8

    going in same direction:
    distance covered by faster = (5/4)x + 1/2 , (1/4 lap is 1/2 km)
    distance covered by slower = (5/4)y

    (5/4)x + 1/2 = (5/4)y
    5x + 2 = 5y
    5x - 5y = -2

    multiply the first by 5
    5x+5y = 40
    5x - 5y = -2
    10x = 38
    x = 3.8
    then y = 4.2

    opposite directions:
    the faster went (1/4)(4.2) = 1.05 km
    the slower went (1/4)(3.8) = .95
    which adds up to 2 km, or 1 lap

    same direction:
    faster went (5/4)(4.2) = 5.25
    slower went (5/4)(3.8) = 4.75
    5.25 - 4.75 = .5 km, or 1/4 of a lap

    all is good

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