A larger pipe can fill a tank in 32 minutes less than a smaller pipe. If they both are turned on, they can fill the tank in 30 minutes. How long does it take each pipe to fill the tank alone?

Let t be the time for smaller pipe

Then t-32 will be the time for larger pipe

In 1 minute both will fil 1/t+1/(t-32)

In 30 minutes it will be full

30 (1/t+1/(t-32)) =1

30 (t-32+t) = t(t-32)

30t -960+30t =t^{2}-32t

Or

t^{2}-92t+960 =0

t^{2}-12t-80t+960+0

t(t-12)-80(t-12)=0

(t-12)(t-80)=0

t-12=0 is not admissible because t-32 will benegative

t =80

Smaller pipe will take 80 minutes to fill the full tank

Larger pipe will take 48 minutes to fill the full tank

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