alanforde800Maximus wrote:

Two painters, Ray and Taylor, are painting a fence. Ray paints at a uniform rate of 40 feet every 160 minutes, and Taylor paints at a uniform rate of 50 feet every 125 minutes. If the two painters paint simultaneously, how many minutes will it take for them to paint a fence that is 260 feet long?

a) 320

b) 400

c) 450

d) 500

e) 580

We are given that Ray paints at a uniform rate of 40 feet every 160 minutes. Thus, the rate of Ray is 40/160= 1/4 ft/min.

We are also given that Taylor paints at a uniform rate of 50 feet every 125 minutes. Thus, the rate of Taylor is 50/125= 2/5 ft/min.

We need to determine the time it will take to paint a fence, that is 260 feet long, when Ray and Taylor work simultaneously.

To determine the time to paint a 260-foot-long fence, we can use the combined work formula:

Work done by Ray + Work done by Taylor = 260 feet (the total work completed)

Because Ray and Taylor are working simultaneously, we can let the time they both work together be t minutes. We now can express the individual work done by Ray and Taylor. We must remember that work = rate x time.

Work done by Ray = (1/4)t

Work done by Taylor = (2/5)t

(1/4)t + (2/5)t = 260

We can multiply the entire equation by 20 to cancel out the fraction and we have:

5t + 8t = 5,200

13t = 5,200

t = 400 minutes

Answer: B

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