word problem help - algebra

[isisgirl28]

I have this problem for homework and have tried a number of ways and cannot find the right equation.

"Mike reads at an average rate of 30 pages per hour, while Susan reads at an average rate of 40 pages per hour. If Mike starts reading a book at 4:30 pm, and Susan begins reading the same book at 5:20 pm, at what time will they be reading the same page?"

I started with trying simple math of when does multiples of 30 and 40 equal each other.
30 40
60 80
90
120 120
This didn't work because the hours do not start at the same time.

I tried to see how many pages per minute:
30/60 = .5 per minute
40/60 = .67 per minute
Then .5 * 20 minutes= 10 pages
then .67*20 minutres=13.4
This did not work.

Then I tired to figure what the equation would be: .5/minute * X=.67/minute *x

I know I am just missing figuring it out.

Can someone point me in the right direction?
THANKS!!!

 

[Mrspi]

I have this problem for homework and have tried a number of ways and cannot find the right equation.

"Mike reads at an average rate of 30 pages per hour, while Susan reads at an average rate of 40 pages per hour. If Mike starts reading a book at 4:30 pm, and Susan begins reading the same book at 5:20 pm, at what time will they be reading the same page?"

I started with trying simple math of when does multiples of 30 and 40 equal each other.
30 40
60 80
90
120 120
This didn't work because the hours do not start at the same time.

I tried to see how many pages per minute:
30/60 = .5 per minute
40/60 = .67 per minute
Then .5 * 20 minutes= 10 pages
then .67*20 minutres=13.4
This did not work.

Then I tired to figure what the equation would be: .5/minute * X=.67/minute *x

I know I am just missing figuring it out.

Can someone point me in the right direction?
THANKS!!!

I think your idea of finding the number of pages per minute is right on track...but I would NOT use decimals.

Mike reads 30 pages per hour, so he reads 30/60 pages per minute, or 1/2 page per minute.

Susan reads 40 pages per hour, so she reads 40/60 pages per minute, or 2/3 page per minute.

Let x = number of minutes AFTER Susan starts reading

Mike started reading at 4:30 p.m., and Susan started reading at 5:20 p.m. That's 50 minutes after Mike started. So, when Susan has read for "x" minutes, Mike will have been reading for 50 + x minutes.

How many pages will Mike have read in 50 + x minutes? He reads at 1/2 page per minute, so in 50 + x minutes, Mike will have read (1/2)*(50 + x) pages.

How many pages will Susan have read in x minutes? She reads at 2/3 page per minute, so in x minutes, Susan will have read (2/3)*x pages.

We are looking for when Mike and Susan will be on the same page.

x minutes after Susan starts reading, Mike will be on page (1/2)*(50 + x) and Susan will be on page (2/3)*x.

They'll be on the SAME page when

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

Solve that for x, and you'll find out how many minutes it takes for them to be on the same page. BUT...be careful! The question asks "at what TIME will they be reading the same page?"

When you know how many minutes it is for them to get to the same page, you'll have to add that number of minutes to the time Susan started reading (5:20 p.m.) to find out the time when they get to the same page.

 

[Loren]

I would use the rate * time = distance formula. The rate is in pages/hour, the time is in hours (you could convert to minutes if you want to) and the distance is number of pages read.

Let t represent time it takes Mike to read the same number of pages that Sue reads.

Mike reads 30t pages.

Sue starts reading 50 minutes or 5/6 of an hour later. So her time reading is t - 5/6.

Sue --- 40(t - 5/6) pages.

Of course, they read the same number of pages.
Are you ok now?

 

[isisgirl28]

THANK YOU BOTH!

I got it now. 7:50 pm - at 100 pages. I was driving my mom crazy with this problem. I can now go to bed - YEAH!

Mrspi - I kept missing the fact that Mike started before Susan. That ties it together. I quickly solved the problem.

Loren - Interesting way to look at a problem - time and distance - pages of book as the distance - how creative. I will remember to use this in future problems.

THANKS AGAIN FOR YOUR HELP!