Question

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?

Answer 1

Answer: Chuck can paint 65 posts per hour.

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.