The first painter can paint a room in 6 hours,and the second painter can paint the same room in 8 hours...?

If the first painter can paint a row in 6 hours, he can paint 1/6 of the room per hour. Similarly, the second painter paints 1/8 of the room per hour.

Working together, they paint 1/6 + 1/8 = 4/24 + 3/24 = 7/24 of room per hour, which equates to finishing the room in 1/(7/24) = 24/7 hours.

I hope this helps!

First painter can paint 1/6 room in 1 hr.

second = = = 1/8 = = = hr

together;

1/6+1/8=14/48=7/24 of the room in 1 hr

then,we would say

1hr 7/24

X 24/24

X=24/7 hrs=3 hrs & 3/7 hr.

God bless you.

let x be the room area to be painted

painter 1 paints at a rate of x/6

painter 2 paints at a rate of x/8

x/6 + x/8 = the combined rate

(8x +6x)/48 = 7x/24

x/(7x/24) = time to paint the room

24/7 = 3.44 hours

24/7 hours, or 3 hours 26 minutes.

1/(1/6 + 1/8) = 1/(8/48 + 6/48) = 1/(14/48) = 1/(7/24) = 24/7

(1 room / 8 hours) * t + (1 room / 6 hours) * t = 1 room

(1/8)t + (1/6)t = 1

Multiply both sides by 8 and 6.

6t + 8t = 48

14t = 48

t = 24/7 hours

7 hours

At the end of 6 hours, they will have completed 1 and 3/4 rooms, or 1.75. So they work at a rate of 1.75 rooms per 6 hours. From there, it is easy to solve for how long it takes them to paint one room.

1.75/6 = 1/X

Cross-multiply to solve for X.

1.75X = 6

X = 6/1.75

X=3.42

6hrs. + 8hrs /2 = 7 hrs.