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

4 L A T E S T R E P L I E S (Newest First)

Ultraglide

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 17T-18T = -90

or -T = -90

This gives T = 90

Gregg

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*(T-1/6T)))). 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 = T-5.

I can simplify further with LCD by having:

3/18T + 10/18T + 4/18T = T-5.

Then simplifying further to:

17/18T = T-5.

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: