SOLUTION: At the beginning of the summer, Maude and Marilyn each earned $26.40 per day from their summer jobs. After a time, Maude was assigned more responsibility and then earned $29.60 per

Question 5685: At the beginning of the summer, Maude and Marilyn each earned $26.40 per day from their summer jobs. After a time, Maude was assigned more responsibility and then earned $29.60 per day. If they each worked 65 days and together earned a total of $3528, how long did Maude work at the higher rate?
Answer by prince_abubu(198) (Show Source): You can put this solution on YOUR website!
Alright. The problem implied that there was a time, we don't know how many days, that they worked together and were paid the same amount per day.

Let's call that time T for together at the same pay. We'll need to come up with an expression that "spits out" how much they earned while working together at the same pay. That would be

<---- $26.40 for both of them combined per day.

Now the problem does say that after they worked together at the same rate, Maude started working with more responsibilities and got a raise to $29.60 per day. How long did she do that for, though? If they worked for 65 days total and time T was before Maude had extra responsibilities, Maude had to have worked at the new rate for 65 - T days. We've got to add $29.60(65 - T) now to our equation:

But we can't forget that Marilyn still worked at $26.40 for the remainder of the time. She also must have worked (65 - T) days while Maude was working at the higher rate. So, Marilyn's earnings during the 2nd portion of the summer is $26.40(65 - T). Our full equation now is

<---- The left side is how much they earned total, so we set that equal to $3528.00. Be careful, though. Keep in mind that the T would be the time they spent working together at the same rate, so solving for T won't get you the answer they're looking for yet.

<--- We simplified the above equation in a few steps to get to this one. Now, all you have to do is solve for T to get the time they worked together at the same rate. Turns out that T = 35 days.

The problem asks for the time Maude worked at the higher rate. If they worked for a total of 65 days and the first part of the summer was 35 days, then 65 - T = 65 - 35 = 30 days. So Maude worked for $29.60 per day for the remaining 30 days of the summer job.

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