Jordan can build a birdhouse in 2 hours. If it takes her sister 3 hours to build a birdhouse, how long will it take them to buil

Question

madreJ [45]

3 years ago

13

Jordan can build a birdhouse in 2 hours. If it takes her sister 3 hours to build a birdhouse, how long will it take them to buil

d a birdhouse together?

Mathematics

2 answers:

miskamm [114] · Answer 1 · 2022-03-12T03:06:46+03:00

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: $\frac{1}{3} + \frac {1}{2} = \frac{2}{6} + \frac{3}{6} = \frac{5}{6}$

To find how long does it take to build a birdhouse: $\frac{ \frac{5}{6}}{1} = \frac{1}{x}$

Set the denominators equal: $\frac{\frac{5}{6}x}{x} = \frac{1}{x}$

Remove the denominators and solve: $\frac{5x}{6} = 1$

Once again set the denominators equal: $\frac{5x}{6} = \frac{6}{6}$

Remove the denominators and solve for x: $5x = 6 \\ \\ x = \frac{6}{5}$

6/5 hours is equal to 72 minutes.