SOLUTION: A certain array of solar cells can generate 6.0 gigajoules(GJ) in 5.0months (under standard conditions). After this array has been operating for 3.0 month , another array of cell

Algebra ->  Customizable Word Problem Solvers  -> Numbers -> SOLUTION: A certain array of solar cells can generate 6.0 gigajoules(GJ) in 5.0months (under standard conditions). After this array has been operating for 3.0 month , another array of cell      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 1055674: A certain array of solar cells can generate 6.0 gigajoules(GJ) in 5.0months (under standard conditions). After this array has been operating for 3.0 month , another array of cells is added which alone can generate 15.0(GJ) in 7.0 months . How many additional months, after the new array has been added, is needed for the total energy generated from both arrays to be 30 GJ?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
The 1st array has a rate of energy generation of
+6%2F5+ GJ/month
The 2nd array has a rate of energy generation of
+15%2F7+ GJ/month
Operating for 3 months, the amount of energy generated
by the 1st array is:
+%28+3%2F5+%29%2A6+=+18%2F5+ GJ
-----------------------------
Let +t+ = time in months for the total energy with
the new array added to equal +30+ GJ
+18%2F5+%2B+%28t%2F5%29%2A6+%2B+%28+t%2F7+%29%2A15+=+30+
Multiply both sides by +35+
+7%2A18+%2B+6%2A7t+%2B+5%2A15t+=+30%2A35+
+126+%2B+42t+%2B+75t+=+1050+
+117t+=+924+
+t+=+7.8974+
7.9 more months are needed for total energy generated
to be 30 GJ
-----------------------
+18%2F5+%2B+%28t%2F5%29%2A6+%2B+%28+t%2F7+%29%2A15+=+30+
+18%2F5+%2B+%287.9%2F5%29%2A6+%2B+%28+7.9%2F7+%29%2A15+=+30+
+3.6+%2B+%28+6%2F5%29%2A7.9+%2B+%2815%2F7%29%2A7.9+=+30+
+3.6+%2B+1.2%2A7.9+%2B+2.1429%2A7.9+=+30+
+3.6+%2B+9.48+%2B+16.9289+=+30+
+30.0089+=+30+
OK
Error due to rounding off, I think
Definitely get another opinion on this
( unless I got it! )