Dan can weed the garden in 4 hours. His brother Mike can weed the garden in 6 hours.?

[sss]

How long will it take them to weed the garden if they work together?

work please

[James]

Dan= 1/4 every hour
Mike= 1/6 every hour

dan+mike=5/12 every hour
2 hours and 24 mins

[Chris L]

Take the reciprocals of both their times, except make the numerators a single variable. Add together to make a sum of 1 (representing 1 complete job):
x/4 + x/6 = 1

Solve for x.
3x/12 + 2x/12 = 12/12
5x = 12
x = 12/5, or 2.4

It will take them 2.4 hours, or 2 hr 24 min.

[jds]

The garden is the same and also the time is the same for both Dan and Mike. The speed of Dan is 1 garden [g] per 4 hours [h] = 1/4 g/h and the speed of Mike is 1/6 g/h

Remember the time [T] is the same for both, so at Dan's speed during time T and at Mike's speed during the same time T, they will cover 1 garden:
T*1/4g/h + T*1/6g/h = 1 g
getting rid of fractions we multiply whole equation by 12 (which has 4 and 6 as factors):
3Tg/h + 2Tg/h = 12 g
5Tg/h = 12g
T=12/5 h = (2 + 2/5) h
Dan and Mike will take 2 hours and 24 minutes to weed the garden