The ratio of Kim’s time to paint a house to Jane’s time to paint a hou
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08 Jul 2021, 19:17
Not sure if this is the correct method, but this is how I got there.....
Time Ratio: Kim(3):Jane (5):Total(8)
Rate Ratio (inverse of time): Kim(5):Jane (3):Total(8)
Next step was to make a separate rate pie for Kim and Jane. I picked a # for work which is a common multiple of 3 and 5, 30
Kim's Work
(Work) (ft) / (Time) (hrs) = Rate
(30 ft) / (3 hrs) = 10 ft per hour
Jane's Work
(Work) (ft) / (Time) (hrs) = Rate
(30 ft) / (5 hrs) = 6 ft per hour
Problem states that together they can paint a house in 10 hrs. Using the work of (30ft) I determined what the combined rate was
(Work) (ft) / (Time) (hrs) = Rate
30 (ft) / (10 hrs) = 3 ft per hour
So combined Kim and Jane can paint 3 ft per hour. The relationship between Kim and Jane rate is 5:3, so of the 3ft per hour Kim makes up (3*(5/8))=15/8 or 1.8ish of the 3ft per hour
Using Kim's new rate of 15/8, I can find how many hours it took her to paint the 30 ft.
(Work (ft) / (Kim's new rate) = Time it takes Kim to finish the project
(30 ft / (15/8) ) = 16 ish , answer D