TWO WORKERS A AND B ARE ENGAGED TO DO A WORK. A WORKING ALONE TAKES 8 HOURS MORE TO COMPLETE THE JOB THAN IF BOTH WORKED TOGETHER. IF B WORKED ALONE, HE WOULD NEED 4 1/2 HOURS MORE TO COMPLETE THE JOB THAN THEY BOTH WORKING TOGETHER. WHAT TIME WOULD THEY TAKE TO DO THE WORK TOGETHER?  Choose the correct choice from the following answers:  A) 4 HOURS  B) 5 HOURS  C) 6 HOURS  D) 7 HOURS  E) NONE OF THESE
LET A AND BE TOGETHER TAKE X HOURS TO COMPLETE THE WORK. THEN, A ALONE TAKES (X+8) HRS AND B ALONE TAKES (X+9/2) HRS TO COMPLETE THE WORK. THEN,   1/(X+8)+1/(X+9/2)=1/X, 1/(X+8)+2/(2X+9)=1/X   X(4X+25)=(X+8)(2X+9)   2X^2=72, X^2=36, X=6   6 HOURSorrect Option : 6 HOURS
<result>C</result>
TWO WORKERS A AND B ARE ENGAGED TO DO A WORK. A WORKING ALONE TAKES 8 HOURS MORE TO COMPLETE THE JOB THAN IF BOTH WORKED TOGETHER. IF B WORKED ALONE, HE WOULD NEED 4 1/2 HOURS MORE TO COMPLETE THE JOB THAN THEY BOTH WORKING TOGETHER. WHAT TIME WOULD THEY TAKE TO DO THE WORK TOGETHER?