Mr Jones takes 4 hours to paint a fence.
Mark his son takes 6 hours to paint the same fence.
How long does it take for them both to paint the fence?
In one hour,
dad paints 1/4 fence
son paints 1/6 fence
together they paint 5/12 fence
so, they paint a whole fence in 12/5 hours, or 2 hrs 24 min
It takes them 10 hours to complete two fences, so to complete one together, it would take 5 hours
To find how long it takes Mr Jones and his son Mark to paint the fence together, we can use the concept of work rates. The work rate is defined as the amount of work (in this case, painting the fence) done per unit of time.
Let's start by calculating the work rate for each person. Mr Jones takes 4 hours to paint the fence, so his work rate is 1 fence per 4 hours (1/4 fence per hour). Similarly, Mark takes 6 hours to paint the fence, so his work rate is 1 fence per 6 hours (1/6 fence per hour).
To find the combined work rate of Mr Jones and Mark, we can add their individual work rates together. So their combined work rate is:
1/4 + 1/6 = 3/12 + 2/12 = 5/12 fence per hour.
Now, to determine how long it takes for them to paint the fence together, we can use the formula:
Time = 1 / Work rate.
Substituting the combined work rate into the formula, we have:
Time = 1 / (5/12) = 12/5 = 2.4 hours.
Therefore, it will take Mr Jones and Mark approximately 2.4 hours to paint the fence together.