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
_________________
5-star rated online GMAT quant
self study course
See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews
If you find one of my posts helpful, please take a moment to click on the "Kudos" button.