Answer
a) Tim 1/5; Tara 1/3
b) Tim d/5 in d days; Tara d/3 in d days.
c) Together, 1/5 + 1/3, or 3/15 + 5/15; a total of 8/15
d) 1 = 8d/15; d = 1.875 or 1 and 7/8.
Work Step by Step
a) Tim can paint a house in 5 days, Tara in 3 days. Tim can paint 1/5 of a house in 1 day. Tara can paint 1/3 of a house in 1 day.
b) In d days, Tim can paint a house in d/5 days and Tara can paint a house in d/3 days.
c) Both together, in one day, can paint 1/5 plus 1/3 of the house. In d days, both together can paint d/5 plus d/3.
d) Set an equation equal to 1 (for the whole house). Tim can paint d/5 and Tara d/3. Add them together with common denominator of 15. So, 1 = 3d/15 + 5d/15. Solve for d and get 1.875 or 1 and 7/8.
