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

Question 415588: 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 ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
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?
:
Let a = time required by the auxiliary engine alone
:
It says." main engine alone on a rocket can consume the allotted fuel supply in
two-thirds the time it takes the auxiliary engine alone.". Therefore:
:
a = time required by main engine alone
:
Let the consumption of the fuel together = 1
:
+ = 1
:
divide 2/3 into 36: 36*(3/2) = 54, so you have
+ = 1
multiply by a
36 + 54 = a
a = 90 sec, Aux engine alone
and
*90 = 60 sec, Main engine alone
:
:
Check this:
36/90 + 36/60 =
.4 + .6 = 1; confirms our solutions

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