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Tom reads at an average rate of 30 pages per hours, while

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Tom reads at an average rate of 30 pages per hours, while [#permalink] New post 18 Jun 2005, 10:26
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Tom reads at an average rate of 30 pages per hours, while Jan reads at an average rate of 40 pages per hour. If Tom starts reading a novel at 4:30, and Jan begins reading an identical copy of the same book at 5:20, at what time will they be reading the same page?

a. 9:30
b. 9:00
c. 8:40
d. 7:50
e. 7:00

When trying to do the factoring...

30 = 2 x 3 x 5
40 = 2 x 2 x 2 x 5

2 x 2 x 2 x 3 x 5 = 120

Tom = 120 / 30 = 4
Jan = 120 / 40 = 3

Now I'm stuck.
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Re: PS: Reading Problem (Factors?) [#permalink] New post 18 Jun 2005, 13:11
tbetten wrote:
Tom reads at an average rate of 30 pages per hours, while Jan reads at an average rate of 40 pages per hour. If Tom starts reading a novel at 4:30, and Jan begins reading an identical copy of the same book at 5:20, at what time will they be reading the same page?

a. 9:30
b. 9:00
c. 8:40
d. 7:50
e. 7:00

When trying to do the factoring...

30 = 2 x 3 x 5
40 = 2 x 2 x 2 x 5

2 x 2 x 2 x 3 x 5 = 120

Tom = 120 / 30 = 4
Jan = 120 / 40 = 3

Now I'm stuck.


Tom reads 30/60 = 1/2 page per minute
Jen reads 40/60 = 2/3 pages per minute

1/2 *(x+50) = 2/3 *x

x = 150 minutes

5:20 + 2 h 30 min = 7:50. or D
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 [#permalink] New post 19 Jun 2005, 15:21
interesting exercises :wink:
would it be possible to solve it this way thanks
30T = 40(t+7/6)

Where T is tom time
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 [#permalink] New post 19 Jun 2005, 15:47
Easier to convert into minutes.

Tom's rate is 1/2 page per min
Jan's rate is 2/3 page per min

Jan reads 2/3 - 1/2 = 1/6 extra pages per minute

When Jan begins, Tom has already read 50/2 = 25 pages.

To catch up, Jan needs 25/(1/6) = 150 additional minutes (2hrs 30 minutes) from when she starts -> She will catch up at 7:50

Answer is D

I'd have solved it like Sparky, but just wanted to try this mehtod out.
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 [#permalink] New post 20 Jun 2005, 03:41
mandy wrote:
interesting exercises :wink:
would it be possible to solve it this way thanks
30T = 40(t+7/6)

Where T is tom time


tom starts 50min earlier. that means t+5/6 more time and at his rate the number of pages he could read would be 30(t+5/6). that means 40t=30(t+5/6). solve for t and you will get 150min.
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 [#permalink] New post 20 Jun 2005, 06:11
It's D.

Thanks guys!

:-)
  [#permalink] 20 Jun 2005, 06:11
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