Secondary 3 E-learning Maths question

[bluesky63]

Hi all Maths guru,


there is a sec3 maths qns (elearning) that I don't understd the steps and working given . The questions is below, I seek somebody who can provide me with easy explaination

Question

Mrs Tan takes 1 day more to finish marking the mathematics exam papers of all the 36 students in her class as compared to Mr Wong. If Mrs Tan marked the papers together with Mr Wong, both of them would complete the marking in 2 days. Find the time, in minutes, Mr Wong would take to mark a paper alone. Correct your answer to 3 sigificant figures

[A] 142 mins [B] 22.5 mins [C] 121 mins [D] 41.0 min

[n00bin4t0r]

All these are in rates (no of papers marked) per hour.

Let x be the number of days Wong takes to mark 36 papers.
Wong’s rate = 36/x
Tan’s rate = 36/(x+1)
Combined rate = (72x+36)/(x(x+1))
Combined duration = 2
Combined duration = 36/Combine rate
36/Combined rate = 2
… solve for x, remember to reject non-logical answers if there are 2 solution
Answer = x/36 (in papers per days) = ??? (in papers per minute)

I’m sure there are many ways to do this, but here’s my thought process.
I have to find Wong’s rate, so I let it be x.
Then, I have to get an equation where x is the only unknown so I can solve it.
A quick scan through & by gut feeling, its the equation that equates to 2.
So, I need the left-hand-side of that equation, the combined duration which requires the combined rate which in turn requires the individual rates of Tan & Wong.
So, I express Tan & Wong’s rate in x, substitute to get their combined rate, then substitute to get combined duration and solve for x

[bluesky63]

Hi

Thanks, l will try it out

n00bin4t0r:

All these are in rates (no of papers marked) per hour.
Let x be the number of days Wong takes to mark 36 papers.
Wong's rate = 36/x
Tan's rate = 36/(x+1)
Combined rate = (72x+36)/(x(x+1))
Combined duration = 2
Combined duration = 36/Combine rate
36/Combined rate = 2
... solve for x, remember to reject non-logical answers if there are 2 solution
Answer = x/36 (in papers per days) = ??? (in papers per minute)

I'm sure there are many ways to do this, but here's my thought process.
I have to find Wong's rate, so I let it be x.
Then, I have to get an equation where x is the only unknown so I can solve it.
A quick scan through & by gut feeling, its the equation that equates to 2.
So, I need the left-hand-side of that equation, the combined duration which requires the combined rate which in turn requires the individual rates of Tan & Wong.
So, I express Tan & Wong's rate in x, substitute to get their combined rate, then substitute to get combined duration and solve for x

[FrekiWang]

one day may not/should not be 24hour x 60min, not realistic