SOLUTION: The main engine alone on a rocket can consume the allotted fuel supply in two-thirds the time it takes the auxiliary engine alone. working together they both consume their allotted

Algebra ->  Rational-functions -> SOLUTION: The main engine alone on a rocket can consume the allotted fuel supply in two-thirds the time it takes the auxiliary engine alone. working together they both consume their allotted      Log On


   

Question 310432: The main engine alone on a rocket can consume the allotted fuel supply in two-thirds the time it takes the auxiliary engine alone. working together they both consume their allotted fuel in 36 seconds. how long could each be fired alone?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let a = alloted fuel
Let t = time auxiliary engine takes to consume alloted fuel
Their rates of consuming fuel are:
main engine:
a%2F%28%282%2F3%29%2At%29
auxiliary engine:
a%2Ft
Both engines together:
a%2F36 sec
-----------------
a%2F%28%282%2F3%29%2At%29+%2B+a%2Ft++=+a%2F36
3a%2F2t+%2B+a%2Ft+=+a%2F36
Multiply both sides by 36t
54a+%2B+36a++=+at
90a+=+at
t+=+90
%282%2F3%29%2At+=+60
The main engine could be fired for 60 sec
The auxiliary engine could be fired for 90 sec