$x is enough for Bob to survive 45 days, while for Amy $x is enough to

Solution

• Let’s assume x as the LCM(45, 36)

o x = 180 units
• The amount required by Bob to survive one day = \(\frac{180}{45} = 4\) units
• The amount required by Amy to survive one day = \(\frac{180}{36} = 5\) units

o The amount required by both of them together to survive one day = \(4 + 5 = 9\) units
o In 180 units they can survive = \(\frac{180}{9} = 20\)days
o With $ \(x\) they can survive = \(20\) days
o With $\(2x\) they can survive =\(2*20=40\) days

Alternative method:

• The amount required by Bob to survive 45 days = x

o The amount required by Bob to survive 1 day = \(\frac{x}{45}\)
• The amount required by Amy to survive 36 days = x

o The amount required by Amy to survive 1 day = \(\frac{x}{36}\)
• Amount required by both of them to survive 1 day = \(\frac{x}{45} + \frac{x}{ 36} = \frac{(5x + 4x)}{180} = \frac{x}{20}\)

o With \(\frac{x}{20}\) they both can survive 1 day
o With \(x\), they can survive for 20days
o With $ \(2x\) they can survive for 40 days