A painter finishes painting a house in 6 hours. Her assistant takes 8 hours to do the same job. How long will it take if they both work together

Answer 1

The painter finishes painting the house in 6 hours.

In other words, his painting rate is one house in 6 hours or 1/6.

The painter's assistant paints the same house in 8 hours.

In other words, his painting rate is one house in 8 hours or 1/8

Therefore,

Painter's (1) painting rate:

r₁ = 1/6

Painter's Assistant (2) painting rate:

r₂ = 1/8

The equation relating the painting rate (r), time (t) and number of houses painted (h):

h = r . t

For example, the number of houses painted by the painter (1) in 6 hours is:

h = r₁.t = 1/6 x 6 = 1

Intuitive, huh! The number of houses painted by the painter AND the painter's assistant in any time is therefore:

h = h₁ + h₂ = r₁.t + r₂.t = (1/6)t + (1/8)t = 8t/(6*8) + 6t/(6*8) = (8+6)t/48 = 14t/48 = 7t/24

Or simply,

h = 7t/24

Rearrangement yields,

t = 24h/7

The time it takes to make the same house with the two painters is therefore:

t = 24/7 or 3.43 hours

=)

So basically to solve a problem like this, you:

(1) find the painters' (could be more than two) rate

(2) use the rates in the equation to find the number of houses (h) painted in a given time OR the time (t) it takes to paint a given number of houses (which is one in this case):

h = (r₁ + r₂)t

OR

t = h/(r₁ + r₂)

Answer 2

t represents the time working together

t/8 + t/6 = 1

Can you solve for t and answer?