SOLUTION: Jessie and Mark are planning to paint a house together. Jessie thinks that if he works alone, it would take him 5 hours more than the time Mark takes a paint the entire house. work

Algebra ->  Rate-of-work-word-problems -> SOLUTION: Jessie and Mark are planning to paint a house together. Jessie thinks that if he works alone, it would take him 5 hours more than the time Mark takes a paint the entire house. work      Log On


   

Question 906861: Jessie and Mark are planning to paint a house together. Jessie thinks that if he works alone, it would take him 5 hours more than the time Mark takes a paint the entire house. working together, they can complete the job in 6 hours.
1. what equation represents the situation?
2. how long would it take Jessie and Mark if each work alone in painting the entire house?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Add their rates of working to get
their rate working together
----------
Jessie's rate:
( 1 house painted ) / ( his time to paint it )
Mark's rate:
( 1 house painted ) / ( his time to paint it )
Working together:
( 1 house painted ) / ( 6 hrs )
--------------------
Let +t+ = Mark's time in hrs to paint house
--------------------------
+1+%2F+%28+t+%2B+5+%29+%2B+1%2Ft+=+1%2F6+
--------------------------
Multiply both sides by +t%2A%28+t%2B5+%29%2A6+
+6t+%2B+6%2A%28+t%2B5+%29+=+t%2A%28+t%2B5+%29+
+6t+%2B+6t+%2B+30+=+t%5E2+%2B+5t+
+t%5E2+-+7t+-+30+=+0+
+%28+t+-+10+%29%2A%28+t+%2B+3+%29+ ( just by looking at it )
+t+=+10+
+t+=+-3+
Time can't be negative, so
+t+=+10+
+t+%2B+5+=+15+
Jessie would take 15 hrs working alone
Mark would take 10 hrs working alone
-------------------
check:
+1+%2F+%28+t+%2B+5+%29+%2B+1%2Ft+=+1%2F6+
+1+%2F+15+%2B+1%2F10+=+1%2F6+
+4%2F60+%2B+6%2F60+=+10%2F60+
+10%2F60+=+10%2F60+
OK