Question 310432
Let {{{a}}} = alloted fuel
Let {{{t}}} = time auxiliary engine takes to consume alloted fuel
Their rates of consuming fuel are:
main engine:
{{{a/((2/3)*t)}}}
auxiliary engine:
{{{a/t}}}
Both engines together:
{{{a/36}}} sec
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{{{a/((2/3)*t) + a/t  = a/36}}}
{{{3a/2t + a/t = a/36}}}
Multiply both sides by {{{36t}}}
{{{54a + 36a  = at}}}
{{{90a = at}}}
{{{t = 90}}}
{{{(2/3)*t = 60}}}
The main engine could be fired for 60 sec
The auxiliary engine could be fired for 90 sec