The ratio of Kim’s time to paint a house to Jane’s time to paint a hou

Question

The ratio of Kim’s time to paint a house to Jane’s time to paint a house is 3 : 5. If Kim and Jane work together at their respective constant rates, they can paint a house in 10 hours. What is the number of hours it takes Kim to paint the house alone?

A. 13
B. 14
C. 15
D. 16
E. 17

A. 13
B. 14
C. 15
D. 16
E. 17

doomedcat · Accepted Answer

Time Kim:Jane = 3:5
time to paint kim = 3x hrs; kim's 1 hr work = 1/3x
time to paint Jane = 5x hrs; jane's 1 hr work = 1/5x

1/3x + 1/5x = 1/10
x=16/3
so kim's time = 3*16/3 = 16 hrs

Aks111 · Answer

Let total area to paint be 30 sq.m.
Let Kim take 3hr to paint 30 sq.m. So, In 1 hr Kim can paint = 30/3 = 10 sq.m
i.e. Rate at which Kim paints = 10 sq.m per hr
Let Jane take 5hr to paint 30 sq.m. So, In 1 hr Jane can paint = 30/5 = 6 sq.m
i.e. Rate at which Jane paints = 10 sq.m per hr
So at the assumed rates they paint 10+6 = 16 sq.m per hr

But it is mentioned they together take 10 hrs to paint.
So, in 1hr together they paint = 30/10 = 3 sq.m

So the assumed rate 16sq.m per hr corresponds to 3sq.m per hr for 30 sq.m area
Hence the actual total area for combined rate of 16 sq.m per hr would be =  \frac{(30 * 16) }{ 3} = 160 sq.m

Rate at which Kim paints = 10 sq.m per hr
Therefore, Total time required by Kim to paint 160 sq.m area = 160/10 = 16 hr

Ans: D

Merlin1411 · Answer

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

Rebaz · Answer

Bunuel

This is not a RTD problem. It is a RTW problem wrongly Catagorized

Bunuel · Answer

Fixed the tag. Thank you!

sherifY · Answer

Friends, also think a very quick way i did it is.

The ratio is 3 to 5 so total is 8. Whatever the answer is, it should be a multiple of 8 -> 16.

What do you think?

ADITHISRINIVAS · Answer

Does this hold true if we were to switch up the values?

Krunaal · Answer

It is not a valid method to solve this problem, the logic is flawed and  "be a multiple of 8 -> 16"  is a mere co-incidence.

Strategix · Answer

Ratio of Kim's time : Jane's time = 3x:5x
Ratio of Kim's rate : Jane's rate = 5x:3x (rate is inverse of time)

When they work together: 8x = 1/10; x =1/80.

Thus Kim's time = 1/5x => 16 hours.

dhruvie · Answer

Time Ratio:  K:J :: 3:5
 Work Ratio:  K:J :: 5:3

Therefore, work done  together  is 5A+3A =  8A Units 
Time taken  together  is  10 hours .

Total work is  80A Units .

Time taken by K is  \frac{80A}{5A}  i.e.  16 hours .

Note: A is just some constant taken here since we are using ratios.

Amity007 · Answer

I tried a different approach
time ratio is 3:5 so the rate of work ratio is 5:3.
Now since they worked for 10 hours, 
 the rate of k would be 5/8 for 10 hours
 >>then for 1 hour rate would be 5/(8*10) -> 1/16 --->> k alone would do in 16 hours
Is this a right approach?

The ratio of Kim’s time to paint a house to Jane’s time to paint a hou

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The ratio of Kim’s time to paint a house to Jane’s time to paint a hou

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