Question

Peter can paint a room in 5 hours, Paul can paint a room in 6 hours, Neil can paint a room in 7 1/2 hours and Mary can paint a room in 3 3/4 hours.

Which two painters above can team up to paint a whole room in 3 hours?

Write and solve a Rational Equation that shows you are correct. Please show your work.

Answer 1

Peter and Neil

Explanation:

Given rates of work:

Peter = 5 hours / room

Paul = 6 hours / room

Neil = 7.5 hours / room

Mary = 3.75 hours / room

Recall the formula for combined rate for two individuals A & B is given as

Combined rate = (A's rate x B's rate) / (A's rate + B's rate)

In our case , the combined rate is given to be 3 hours, so we must find a combination of rate A and rate B that will give us 3 hours.

If you try all the combinations in the above formula, we will find that if we substitute Peter's and Neil's rates into the formula, we will get exactly 3 hours.

Combined rate for Peter and Neil

= (Peter's rate x Neil's rate) / (Peter's rate + Neil's rate)

= (5 x 7.5) / (5+7.5) = 3 hours to complete 1 room

No other combination gives exactly 3 hours.

Answer 2

paul and mary

peter and mary

peter and paul