Quadratic Equations

Asked by aruni_maiyer | 18th May, 2010, 07:42: PM

Expert Answer:

Given 2 8/11 = 30/11

Let q1, q2 be the flow rates from two pipes, and cistern volume be V.

t1 = V/q1 and t2 = V/q2

t1 + 1 = t2              ..... given than one pipe takes 1 min more to fill the cistern.

t = V/(q1 + q2)             ... time to fill the cistern together.

30/11 = V/(q1 + q2)

30/11 = 1/(q1/V + q2/V)

30/11 = 1/(1/t1 + 1/(t1 + 1))

30/11 = t1(t1 + 1)/(2t1 + 1)

60t1/11 + 30/11 = t1(t1 + 1)

60t1/11 + 30/11 = t12 + t1

t12 - 49t1/11 - 30/11 = 0

Solving this quadratic equation we find,

t1 = (49/11 ± 61/11)/2

t1 = 110/22 = 5 min and hence t2 = 6 min.

Hence the times in which each pipe will fill the cistern are 5 and 6 min respectively.

Regards,

Team,

TopperLearning. 

Answered by  | 19th May, 2010, 11:38: AM

Queries asked on Sunday & after 7pm from Monday to Saturday will be answered after 12pm the next working day.