Jonathan can paint a room in 8 hrs. After painting for 2 hours, his brother, David joined him and together, they finished painting the room in 3 1/3hours. In how many hours will David finish painting the room alone?
Jon's rate ---- room/8
David's rate --- room/x
combined rate = room/8 + room/x
= (xroom + 8room)/(8x)
= room(x+8)/(8x)
but only (3/4)room remains to be painted.
so ..
(3/4)room/( (room(x+8)/(8x) ) = 10/3
(3/4) (8x)/(x+8) = 10/3
72x = 40x + 320
32x = 320
x = 10
Working alone he could have done the whole room in 10 hours, so it would take him 7.5 hours to finish the room
To solve this problem, we can first calculate how much work Jonathan does in 2 hours by dividing the total time he takes to paint the room (8 hours) by the number of hours he worked (2 hours):
Jonathan's work rate: 1 room / 8 hours = 1/8 room per hour
Work done by Jonathan in 2 hours:
Work rate x Time = (1/8 room per hour) x 2 hours = 1/4 room
Next, we need to find out how much work David and Jonathan together did in the remaining time (3 1/3 hours - 2 hours = 1 1/3 hours). Since together, they can finish the room in 3 1/3 hours, we'll calculate their combined work rate in terms of room per hour:
Combined work rate: 1 room / (3 1/3 hours) = 3/10 room per hour
Work done by David and Jonathan together in 1 1/3 hours:
Work rate x Time = (3/10 room per hour) x (4/3 hours) = 1/5 room
Now, to find out how much work David did alone, we subtract the work done by Jonathan from the work done by both of them:
Work done by David alone:
Work done by David and Jonathan - Work done by Jonathan = 1/5 room - 1/4 room
To subtract fractions, we need to find a common denominator, which is 20 in this case:
(4/20) - (5/20) = -1/20
Since the result is negative, it means David did not contribute to the work, so we conclude that David did not paint the room alone.
However, if we assume that David does paint the room alone, we calculate his work rate using the equation (work rate x time = work done):
David's work rate = (1 room) / (x hours)
Given that the work done by David alone is 1/5 room, the equation becomes:
(1/5 room) = (1 room) / (x hours)
To find x, we cross-multiply and solve for x:
1 * x = 1/5 * 1
x = 5/1
x = 5
Therefore, based on these calculations, David would finish painting the room alone in 5 hours.