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9 May, 20:44

Theresa has hired Chuck and Diana to paint a fence. Diana can paint 150 fence posts in the same time it takes Chuck to paint 130 fence posts, which can be shown using the following relationship where d and c are the respective rates at which Diana and Chuck can paint fence posts: 150 over d equals 130 over c Also, Diana can paint 10 fence posts more per hour than Chuck. How many fence posts can Chuck paint per hour?

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  1. 9 May, 21:02
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    Answer: Chuck can paint 65 posts per hour.

    Step-by-step explanation:

    The data we have here is:

    Diana can paint 150 fence posts in a time T

    Chuck can pint 130 fence posts in a time T.

    In one hour, Diana can paint 10 more fence posts than Chuck.

    If D is the hourly rate of Daian, and C is the hourly rate for Chuck, we have:

    D = 150/T

    C = 130/T

    D = C + 10

    we can replace the last equation in the first one and geT:

    C + 10 = 150/T

    C = 130/T

    Now we can replace the bottom equation in the above one:

    130/T + 10 = 150/T

    10 = 150/T - 130/T = 20/T

    T*10 = 20

    T = 20/10 = 2

    So T is 2 hours, then whe have:

    D = 150post/2hours = 75 posts per hour.

    C = 130 posts/2hours = 65 posts per hour.
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