Can anybody help me with this? I don't understand?:
Tim paints 1 fence every two minutes. Moby paints 14 fences every two minutes. How many minutes will it take them to paint the fences, working together, if they have 150 fences to paint.
1/2 + 2/14 = x/150
http://www.purplemath.com/modules/workprob4.htm
2/1+14/2=150/x
Here is a common sense approach. In two minutes, they both paint 15 fences.
amount=rate*time
150fences=15fences/2min * time
time= 150*2/15=20 min
Now a more analytical approach.
The combined rate is the rate of each added.
ratecombined= 1fence/2min+14fence/2 min
= 15fence/2 min
fencestotal= ratecombined*time
150=15/2 * time and you have it.
opps! be sure to write the units out because I accidentally wrote 2 min/1 fence instead of 1 fence/ 2 min.
1 fence/2 min +14 fence/2 min= 150 fence/x min
To find out how long it will take Tim and Moby to paint the fences together, we need to calculate their combined painting speed.
Tim paints 1 fence every two minutes, so his painting rate is 1 fence per 2 minutes. Similarly, Moby paints 14 fences every two minutes, which means his painting rate is 14 fences per 2 minutes.
To compare their painting rates, we need to have the same unit of time, so let's convert their rates to fences per minute. To do this, we divide the fences they paint in 2 minutes by 2, since we're converting to per minute.
For Tim:
1 fence in 2 minutes = (1/2) fence per minute
For Moby:
14 fences in 2 minutes = (14/2) fences per minute = 7 fences per minute
Now we can calculate their combined painting rate by adding Tim's and Moby's rates:
Combined rate = Tim's rate + Moby's rate
Combined rate = (1/2) fence per minute + 7 fences per minute
Combined rate = (1/2 + 7) fences per minute
Combined rate = (8/2) fences per minute
Combined rate = 4 fences per minute
Since we know their combined painting rate is 4 fences per minute, and they need to paint 150 fences, we can calculate the time it will take them.
Time = Number of fences / Combined rate
Time = 150 fences / 4 fences per minute
Time = 37.5 minutes
Therefore, it will take Tim and Moby approximately 37.5 minutes to paint the 150 fences working together.