martha can paint a room in 2hours. Jamie can paint the same room in 6 hours. How long to the nearest tenth of an hour will it take it them to paint the room

Step-by-step explanation:

If you multiply the speed of housepainting (houses/hour) by the number of hours, you get the number of houses, because the hours units cancel out.

John and Sally, when painting together, are painting for the same amount of time, let's call that T.

Then the total amount of houses that John paints in time T is T x 1/6 = T/6, because he paints 1 house in 6 hours alone.

The total amount that Sally paints is T x 1/4 = T/4 for the same reason.

So the total amount of houses they paint together is T/6 + T/4. But you know they together paint exactly one house in that time, so:

1 = T/6 + T/4.

If you now solve for T, you will have your time (expressed in hours,

so you may need to calculate the minutes from the fractional part

of the answer).

Without algebra:

Sally can paint a house in 4 hours so she paints an the rate of 1/4 of a house per hour.

John can paint a house in 6 hours so she paints an the rate of 1/6 of a house per hour.

Thus together they paint at the rate of 1/4 + 1/6 of a house per hour.

Express this sum as a single fraction. At that rate how long does it take to paint 1 house?