working at different rates

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Presentation transcript:

working at different rates

Working alone, Dick can paint the house in 10 days. Working alone, Jane can paint the house in 6 days. How many days will it take them to paint the house working together?

Working alone, Dick can paint the house in 10 days. Working alone, Jane can paint the house in 6 days. How many days will it take them to paint the house working together?

IN ONE DAY Working alone, Dick can paint the house in 10 days. Working alone, Jane can paint the house in 6 days. IN ONE DAY He paints 1/10 of the house and She paints 1/6 of the house

IN TWO DAYS Working alone, Dick can paint the house in 10 days. Working alone, Jane can paint the house in 6 days. IN TWO DAYS He paints 2/10 of the house and She paints 2/6 of the house

IN THREE DAYS Working alone, Dick can paint the house in 10 days. Working alone, Jane can paint the house in 6 days. IN THREE DAYS He paints 3/10 of the house and She paints 3/6 of the house

Let x = the number of days it will take them to Working alone, Dick can paint the house in 10 days. Working alone, Jane can paint the house in 6 days. Let x = the number of days it will take them to paint the whole house working together. IN THREE DAYS He paints 3/10 of the house and She paints 3/6 of the house

IN x DAYS Working alone, Dick can paint the house in 10 days. Working alone, Jane can paint the house in 6 days. IN x DAYS He paints x /10 of the house and She paints x /6 of the house

IN x DAYS Working alone, Dick can paint the house in 10 days. Working alone, Jane can paint the house in 6 days. The fraction of the house that he paints + The fraction of the house that she paints =1 IN x DAYS He paints x /10 of the house and She paints x /6 of the house

IN x DAYS Working alone, Dick can paint the house in 10 days. Working alone, Jane can paint the house in 6 days. The fraction of the house that he paints + The fraction of the house that she paints =1 The equation: x/10 + x/6 = 1 IN x DAYS He paints x /10 of the house and She paints x /6 of the house

The equation: x/10 + x/6 = 1

The equation: x/10 + x/6 = 1 After 3 ¾ days the job is finished.