SOLUTION: Hello, I would appreciate any help you could give me with the following word problem/inverse variation. It takes 7 hrs for Mary to rake leaves by herself, but her brother Matt can

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Question 1018421: Hello, I would appreciate any help you could give me with the following word problem/inverse variation. It takes 7 hrs for Mary to rake leaves by herself, but her brother Matt can work three times as fast. If they work together, how long will it take them to rake leaves. I have a chart to complete with rate, time and work done for each sibling. I have Mary: rate 1/7, time 7, work done, 1. Matt: rate 3/7, time 3, and /work done 1. together rate is 1/7 +3/7=4/7=7/4= 1.75 or 1 hour and 45 minutes. Thank you!
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
You can add their rates of working to
get their rate working together.
Mary's rate can be expressed as:
[ 1 job ] / [ 7 hrs ]
Matt's rate is:
[ 3 jobs ] / [ 7 hrs ]
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Note that this is exactly the same as:
[ 1 job ] / [ 7/3 hrs ]
it's just 2 ways to look at the same thing
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Let +t+ = time in hrs for them to complete
the leaf-raking job working together
Their rate working together is:
[ 1 job ] / [ t hrs ]
--------------------------
I can say:
+1%2F7+%2B+3%2F7+=+1%2Ft+
+4%2F7+=+1%2Ft+
Multiply both sides by +7t+
+4t+=+7+
+t+=+7%2F4+ hrs
+7%2F4+=+1+%2B+3%2F4+
1 hr 45 min
You did the same thing a little differently