Author 
Topic 

Gregg
Junior Member
USA
3 Posts 
Posted  03/09/2012 : 13:32:47

Hello;
this is a 5th grade math problem. It has fractions in it and also seems like it could be solved with algebra.
it takes ben 1/6 of his time to complete task 1. then he needs 2/3 of the remaining time to complete task 2. finally it takes him 4/5 of his remaining time to complete the final task. he completes all tasks with 5 mins remaining. how long did it take ben to complete all tasks?
Here's how I've tried to express it so far. I think I want to solve for T. I'm not sure how to go forward from here.
(1/6*T) + (2/3*(T(1/6*T)))+(4/5*(2/3*(T(1/6*T)))) where T equals Total Time. The solution would then be 5 minutes less than T but I don't know how to simplify and solve the equation.
Thank you, Gregg



royhaas
Moderator
USA
3059 Posts 
Posted  03/09/2012 : 15:27:13

Set it equal to T5. 


Gregg
Junior Member
USA
3 Posts 
Posted  03/09/2012 : 18:13:48

Thank you for your reply. Do you mean like this?
(1/6*T) + (2/3*(T(1/6*T)))+(4/5*(2/3*(T(1/6*T)))) = T5
Can I simplify the whole expression, tho? Would I then need to add +5 to both sides in order to get one side to equal T?
Based on the information in the problem, can I determine the actual total time or is the final answer just T5 and T goes unsolved?
Thank you, Gregg
quote: Originally posted by royhaas
Set it equal to T5.



Gregg
Junior Member
USA
3 Posts 
Posted  03/10/2012 : 14:59:42

Hello;
I have an update and more questions.
I've been working this problem for the past two days. I found an error with my original expression that caused a problem. The third task should be expressed as (4/5*(T((1/6*T))+(2/3*(T1/6T)))). That is, the 4/5 should be multiplied against the sum of the time to complete the first two tasks.
So then if the equation were simplified, it looks like this:
1/6T + 5/9T + 2/9T = T5.
I can simplify further with LCD by having:
3/18T + 10/18T + 4/18T = T5.
Then simplifying further to:
17/18T = T5.
At this point I got stuck. I used an Excel spreadsheet to start experimenting with numbers and focused on those divisible by 6.
Eventually I found that if T = 90, the solution would work.
My problem though is that I still don't know to solve for T in the above expression. How can I get from:
17/18T = T  5 to T=90
?????????
Thanks, Gregg
=4/5*(E1((1/6*(E1))+(5/9*(E1))))
quote: Originally posted by Gregg
Thank you for your reply. Do you mean like this?
(1/6*T) + (2/3*(T(1/6*T)))+(4/5*(2/3*(T(1/6*T)))) = T5
Can I simplify the whole expression, tho? Would I then need to add +5 to both sides in order to get one side to equal T?
Based on the information in the problem, can I determine the actual total time or is the final answer just T5 and T goes unsolved?
Thank you, Gregg
quote: Originally posted by royhaas
Set it equal to T5.



Ultraglide
Advanced Member
Canada
299 Posts 
Posted  03/28/2012 : 00:14:28

To solve the final equation you can remove the ratio by multiplying through by the denominator, in this case 18
(17/18)T(18) = T(18)5(18)
which gives 17T = 18T  90
or 17T18T = 90
or T = 90
This gives T = 90 



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