To find the total work of two people at different speeds, we need to find a common speed limit to both.
In this case, Jordan can build a birdhouse in 2 hours so her speed is 1/2 birdhouse per hour.
For the sister, it takes 3 hours to build a birdhouse so her speed is 1/3 birdhouse per hour.
To find what they can do in one hour: [tex] \frac{1}{3} + \frac {1}{2} = \frac{2}{6} + \frac{3}{6} = \frac{5}{6} [/tex]
To find how long does it take to build a birdhouse: [tex] \frac{ \frac{5}{6}}{1} = \frac{1}{x} [/tex]
Set the denominators equal: [tex] \frac{\frac{5}{6}x}{x} = \frac{1}{x} [/tex]
Remove the denominators and solve: [tex] \frac{5x}{6} = 1 [/tex]
Once again set the denominators equal: [tex] \frac{5x}{6} = \frac{6}{6} [/tex]
Remove the denominators and solve for x: [tex] 5x = 6 \\ \\ x = \frac{6}{5} [/tex]
6/5 hours is equal to 72 minutes.
