Algebra word problem- help please!?
It's been a long time since I took algebra and I need help for my son's homework.
If Hayden can paint a fence in 8 hrs and Dalton can paint the same fence in 10 hours, how long will it take them to get the job done working together?
Need to show work. He is using these tables involving the variable "t" for "time" So it should have the rate of each boy- like 1/8 and 1/10 respectively. Or something like that! We think the answer is 3 or something close, but we need to show the work and the equation and I don't know, lol!
Update:Thank you! We got as far as the 9/40 hr and then weren't sure what to do. He has these boxes to fill in with
H ____|____|____
D ____|____|____
??
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you're on the right track
Hayden can paint 1/8 in an hour
Dalton can paint 1/10 in an hour
together they can paint (1/8) + (1/10) in an hour
1/8 + 1/10 = 5/40 + 4/40 = 9/40 per hour
if they can paint 9/40 of the fence per hour, it will take 40/9 hours, or 4.44 hours working together
with equation goodness:
t(1/8 + 1/10) = 1
where t is the time in hours
t = 1 / (1/8 + 1/10) = 1 / (9/40) = 40/9
t = 4 4/9 = 4.44 hours
Edit: my guess is those boxes are for the total painted by each painter after each hour
H | 1/8 (5/40) | 2/8 (10/40) | 3/8 (15/40) | 4/8 (20/40) |
D| 1/10 (4/40) | 2/10 (8/40) | 3/10 (12/40) | 4/10 (16/40) |
Total | 9/40 | 18/40........| .....27/40........ |...36/40....|
they'll have finished at the 5th hour== 45 / 40...
H = 1 fence in 8 hours, so 1/8 fence in 1 hour.
D = 1 fence in 10 hours, so 1/10 fence in 1 hour.
H+D = 1/8 + 1/10 in 1 hours = 10/80 + 8/80 = 18/80 = 9/40 fence in 1 hours.
x times 9/40 = 1 fence
x = 40/9 hours = 4 hours 26 min 40 sec
Hayden can paint a fence in 8 hrs
=> in 1 hr he paints 1/8th of a fence
=> in 1 hr, dalton paints 1/10 of a fence
If they work together, in 1 hr, both of them will complete (1/8+1/10)th of the fence => 18/80= 9/40th of the fence.
9/40th of fence --- 1 hr
1 fence --- x
x=40/9= 4.44 hrs