The width of the cabinet

Question

A cabinet has two sliding doors of different sizes. When the cabinet is fully closed, they overlap by two-fifths of the width of the smaller door. When both doors are slid to one side, the part of the longer door that is not behind the shorter one is half as wide as the original overlap, and the open portion of the cabinet is 36 inches wide. What is the width of the whole cabinet?

Answer 1

So when both sliding doors are on the same side, the longer one is 1/5 longer than the smaller.

 

Therefore L = (6/5)w where L is the length of the longer door and w is the width of the smaller door

 

When fully closed, they overlap by 2/5 the width of the smaller, so the total length of the

cabinet is (9/5)w

 

which is the same as 36+(6/5)w when both doors are on the same side.

 

(9/5)w = 36 + (6/5)w

 

 (3/5)w = 36

 

w = 60

 

So the smaller door is 60 inches wide and the larger door is 72 inches wide

The width of the cabinet is 108 inches

 

 

Answer 2

When both doors are slid to one side, the longer door covers all but 36 inches.  Which means that when closed, the shorter door covers that amount with 2/5 of it overlapping the large door.  So 3/5 of it it 36 inches long.  Set up a proportion:

 

3/5 = 36/x

3x = 180

x = 60

 

So the shorter door is 60 inches long.  The longer door is 60 inches plus one-half the original overlap.

 

original overlap = 60 - 36 = 24

 

So the longer door is (60 + 12) 72 inches.  So the width of the cabinet is the longer door plus the amount it doesn't cover.

 

72 + 36 = 108 inches