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25 December, 08:24

Some kids went on a bike ride. The ride was six hours long and the kids traveled 54 miles. For part of the ride they biked at a speed of 7 miles per hour and for part of the ride they biked at a speed of 11 miles per hour. For how long did they bike at the first speed and for how long at the other speed?

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  1. 25 December, 08:32
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    Step-by-step explanation:

    The total distance they travel is 54miles

    And the total time taken for the travel is 6hours.

    First part of the journey

    They traveled at speed 7miles/hour

    Let the time for this period be t

    Given that, speed = distance / time

    Then, distance = speed * time

    Also, let the distance covered for this journey be y

    Since, d = s*t

    y=7t Equation 1

    Part two of the journey

    They travel at speed 11miles/hour

    If the time they spend in the first journey is t and the total time for the journey is 6hours, then the time for the second part of the journey is (6-t) hours

    Also, if for the first part of the journey he traveled a distance of y and the total distance for the journey is 54miles, then he traveled 54-y miles for the second part

    Given that, speed = distance / time

    Then, distance = speed * time

    54-y=11 (6-t)

    54-y=66-11t

    11t-y=66-54

    11t-y=12 Equation 2

    Substitute equation 1 into 2. y=7t

    11t-y=12

    11t-7t=12

    4t=12

    t=3hours

    Then the time for the first part of the journey is 3hours

    The time for the second part is given as (6-t) = 6-3=3hours

    Then, the time for the first part and second part are equal which is 3hours
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