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

Algebra ->  Percentage-and-ratio-word-problems -> SOLUTION: A certain array of solar cells can generate 6.0 GJ in 5.0 months (under standard conditions). After this array has been operating for 3.0 months , another array of cells is adde      Log On


   

Question 1055496: A certain array of solar cells can generate 6.0 GJ in 5.0 months (under standard conditions). After this array has been operating for 3.0 months , 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 Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Find the rate of both arrays,
R%5B1%5D%2A5=6
R%5B1%5D=6%2F5
and
R%5B2%5D%2A7=15
R%5B2%5D=15%2F7
So after 3 months, array 1 has generated,
%286%2F5%29%2A3=18%2F5
So then both together need to generate X to reach 30.
18%2F5%2BX=30
X=150%2F5-18%2F5
X=132%2F5
So then together,
%28R%5B1%5D%2BR%5B2%5D%29t=132%2F5
%286%2F5%2B15%2F7%29t=132%2F5
t=%28132%2F5%29%2F%286%2F5%2B15%2F7%29
t=%28%28132%2F5%29%287%2F7%29%29%2F%28%286%2F5%29%287%2F7%29%2B%2815%2F7%29%285%2F5%29%29
t=%28924%2F35%29%2F%2842%2F35%2B75%2F35%29
t=%28924%2F35%29%2F%28117%2F35%29
t=924%2F117
t=308%2F39 or approximately 7.9 months.