how do i do this?

Question

Mark can paint a wall in 5 hrs. Jim can paint the same wall in 3 hrs. How long would it take them to paint the wall if they worked together?

please include the answer and the way u found it. thanks!

Answer 1

let's put x as the number of hours it takes them to paint the room. Jim paints 1/3 of the room every hour, and Mark 1/5 of the room.
so in x hours, they together paint x/3 + x/5 of the room.
you need x/3 + x/5 = 1, because you want the whole room...

the common denominator is 15, and you get
5x/15 + 3x/15 = 1
8x/15 = 1
x= 15/8 = 1+7/8 of an hour.

Answer 2

In 15 hrs. Mark can paint 15/5 = 3 walls and Jim can paint 15/3 = 5 walls, so together they can paint 3 + 5 = 8 walls in 15 hrs. This means that one wall takes them 1/8 as long, or 15/8 = 1 7/8 hrs.

Answer 3

Let x be the fraction of the wall that Mark paints. Then 1-x is the fraction that Jim paints.

The time that Mark will spend painting is x walls * 5 hrs/wall = 5x hrs.

The time that Jim will spend is (1-x) walls * 3 hrs/wall = 3(1-x) hrs.

The time both spend should be equal, so 5x=3(1-x).

Solve for x. You get 8x=3, so x=3/8. That means Mark will paint 3/8 of the wall, and Jim will paint the other 5/8. The time that Mark will spend is 3/8 walls * 5 hrs/wall = 15/8 hours. So that is how long the job will take both of them.

Answer 4

Jim is working at 1.66667 times the rate of Mark i.e. 5/3. So if the area of the wall is one hundred yards square, Jim will paint an area equal to 100 yards sq. divided by (1+1.66667) and multiplied by 1.16667. or (100/2.666667)*1.66667= 67.5 sq. yards. Jim will paint this area in the same time it takes Mark to paint an area equal to (100/2.666667)*1= 37.5 sq. yards. If you add these two figures together they will equal one hundred (or the area of the wall). So now given that it took mark 5 hours to paint 100 sq yards (which is a rate of 20 sq yards an hour 100/5). The time it will take him to paint his 37.5 sq. yards is 37.5/20 or 1.875 hours which is equal to 1 hour 52 minutes and 30 seconds.

Answer 5

Since the task (of painting the same wall) is the same;
5 Mark-hours (M) = 3 Jim-hours (J)
.
When both get togehter, they finish task in x hours.
This task takes : X Mark-hours + X Jim-hours
= x ( M + J)
Since the tasks are the same (Individually or jointly)
x(M+J) = 5M = 3J
take first two parts of the equation:
x(M+J) = 5M
Since 5M = 3J
J=5M/3
.
Hence: x(M+5M/3) = 5M
x=1 7/8 hours

Answer 6

Work done by Mark in 1 hour =1/5........i
Work done by Jim in 1 hour =1/3.......ii
Work done by both in one hour = 1/5 + 1/3
=(3 +5)/15=8/15
Since 8/15 work is done by both in = 1 hour
Therefore 1 work is done =15/8 hours=1.875 hours

Answer 7

i say 2 hrs