two filing pipes p and q are fitted to a tank p is first opened for half the time - Maths - Direct and Inverse Proportions

Question

two filing pipes p and q are fitted to a tank p is first opened for
half the time taken by Q alone to fill the tank and then closed Q
is then open for half the time taken by P alone to fill the tank If
the tank is full after a total of 6 hours after p was opened, for
how long was Q opened?

Shruti Tyagi · Accepted Answer

Dear Student,

let time taken by P to fill tank =x hourstime taken by Q to fill the tank=y hourslet total work =LCMX,Y=xywork done in 1 hour by P=xyx=ywork done by Q in 1 hour=xnow P worked first for half the time taken by q i
e
 y2hence work completed by P in y2 hours=y×y2=y22work done by Q in half time taken by P=x×x2now it is given that work was done after 6 hours when P was openedhence y2+x2=6⇒x+y=12Also since the work is completed the work done by P and Q should be equal to total work i
ey22+x22=xy⇒x2+y2=2xy⇒x2+y2-2xy=0⇒x-y2=0⇒x=yhence x=6 and y=6hence both the pipes P and Q worked equally for 62= 3 hoursHence answer is 3 hours
Regards,

two filing pipes p and q are fitted to a tank .p is first opened for half the time taken by Q alone to fill the tank and then closed . Q is then open for half the time taken by P alone to fill the tank. If the tank is full after a total of 6 hours after p was opened, for how long was Q opened?