sally can paint a room in 7 hours while it takes steve 5 hours to paint the same room. how long would it take to paint the room if they worked together

Answer 1

Hi, Erin!

This is a combined rate problem. The conceptual formula for combined rates is as follows:

(first task completion rate)(time to complete combined task)

+

(second task completion rate)(time to complete combined task)

=

one completed task

This can be written more simply as (r)(t) + (r)(t) = 1. Note, each rate will represent (number of tasks completed) ÷ (time it takes to complete that task). So here, Sally's rate = (1 completed room) ÷ (7 hours), and Steve's rate = (1 completed room) ÷ (5 hours).

This allows us to set up the following:

(1/7)t + (1/5)t=1

From here, use Algebra 2 methods to solve.

1) Rewrite as (t/7) +(t/5)=1

2) Multiply out the common denominator. (7•5)[(t/7) +(t/5)=1] ---> 5t + 7t = 35

3) Use basic algebra to solve. 5t + 7t = 35 --> 12t =35 --> t=35/12 ≈ 2.9167

4) Make your conclusion with the proper units. It will take Sally and Steve approximately 2.9 hours to paint the room together.

Hope that helps!

Katie

Answer 2

Good question, I really disliked these questions when I was younger. However, it's not that bad if you know how to look at it.

The question is phrased as hours per room, which can be misleading, because you need to think about the problem in terms of rooms per hour.

Sally can paint 1 room / 7 hours = 0.143 rooms / hour

Steve can paint 1 room / 5 hours = 0.200 rooms / hour

Together they can paint 0.343 rooms / hour

At that rate it takes 2.9166... hours for them to paint the room together.

Let me know if you have other questions or need clarification.