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PostPosted: Fri Aug 02, 2019 3:25 pm 
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Q17) Matthew reads at an average rate of 30 pages per hour while Alex reads 40 pages per hour. If Mathew start at 4.30 and Alex begins at 5.20 what time will they both be reading the same page??


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PostPosted: Fri Aug 02, 2019 4:22 pm 
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I'm assuming that for 11+ you're expected to solve this by trial and adjustment?

However, to solve by algebra, let's define 't' as the number of hours after 5.20 that they both reach the same page.

Matthew reads an additional 50 minutes (5/6 of an hour) to Alex so:

30(t + 5/6) = 40t
30t + 25 = 40t
10t = 25
t = 2.5 hours

So the time that they both reach the same page is 5.20 plus 2.5 hours = 7.50.


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PostPosted: Fri Aug 02, 2019 5:11 pm 
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I would calculate how many pages they read in a certain number of minutes.
As far as I can see the easiest whole number of pages in the shortest amount of time is 15 for Matthew in 30 minutes and 20 for Alex in 30 minutes.
So then I would keep adding Matthew's 30 minutes blocks - he reads 15 pages by 5pm, 30 pages by 5.30, 45 pages by 6pm, 60 pages by 6.30, 75 pages by 7, 90 pages by 7.30, 105 pages by 8.
Alex has read 20 pages by 5.50, 40 pages by 6.20, 60 pages by 6.50, 80 pages by 7.20, 100 pages by 7.50.
Then I'd go back and say that Matthew reads 5 pages in 10 minutes so he's read 95 by 7.40 and 100 by 7.50 so both he and Alex are on the same page at that point.
My way is more laborious but doesn't require anything other than relatively straightforward maths (albeit a lot of time and a lot of opportunities for silly mistakes).


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PostPosted: Fri Aug 02, 2019 7:27 pm 
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Joined: Mon Dec 24, 2018 3:27 pm
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Sulikhan wrote:
Q17) Matthew reads at an average rate of 30 pages per hour while Alex reads 40 pages per hour. If Mathew start at 4.30 and Alex begins at 5.20 what time will they both be reading the same page??


I have another way.

Alex has head start of 50 minutes so he reads 25 page before Mathew starts.

Every hour Mathew can catch up 40-30=10 pages so 25 pages he needs 2h30 minutes.


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