Question

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2 water tanks together fill a tank in 9 3/8 hrs. The tap of larger diameter takes 10 hrs less than smaller 1 to fill the tank seperately . Find the time in which each tap can seperately fill the tank?​

Answer 1

Step-by-step explanation:

The time taken by smaller tap of diameter to fill the tank seperately =x hours.

Time taken by tap of larger diameter to fill the tank seperately=x-10 hours

The part of the tank filled by tap of smaller diamy in 1 hour=1/x

The part of the tank filled by tap of larger diameter in 1 hour=1/x-10

Given,the two taps together can fill the tank in 75/8 hours

So 75/8/x +75/8/x-10 =1

75/8(1/x-1/x-10)=1

75/8(x-10+x/(x-10)x)=1

75(2x-10)=8(x^2-10x)

150-750=8x^2-80x

8x^2-230x+750=0

4x^2-115x+375=0

By solving the quadratic equation we get,

Time taken by tap of smaller diameter to fill the tank=25hours

Time taken by tap of larger diameter to fill the tank=25-10=15hours