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6 October, 14:50

A cyclist traveled to 11 kilometers per hour faster than an in-line skater. In the time it took to travel 18 kilometers the skater had gone 9 kilometers. Find the speed of the skater

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  1. 6 October, 15:44
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    The speed of the skater is 11 km/h.

    Step-by-step explanation:

    Let v represent the speed of the skater. If we use the formula x = vt, where x is the distance, v is the speed, and t is the time:

    9 = vt (1)

    Since the cyclist traveled to 11 kilometers per hour faster than the skater, the speed of the cyclist is v+11 and time is same for both:

    18 = (v+11) t (2)

    From the equation 1, t = 9/v

    From the equation 2, t = 18 / (v+11)

    Since the t's are equal:

    → 9/v = 18 / (v+11)

    → 9 (v+11) = 18v

    → 9v + 99 = 18v

    → 9v = 99

    → v = 11
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