Math Geniuses!! PLEASE help me!!!?

Question

Write an equation that can be used to solve the problem. Solve the equation and answer the question. Jan and Rhonda own a home remodeling business. they are putting the finishing touches on a home they restored. working alone, jen can paint one room in 4 hours. rhonda can paint the same room in 5 hours. how long will it take them to paint the room if they work together?

Is the answer x/4 + x/5 = 1; 2.22 hr ? if it is how come there are numbers in the denominator and not in the numerator?

Answer 1

Yes, that's correct.

Jen can paint the room in 4 hours, so per hour she can paint (number of rooms) / (time) = 1/4 of a room.
Similarly, in one hour Rhonda can paint 1/5 of the room.

So, after x hours at the same rate, Jen has painted x(1/4) and Rhonda has painted x(1/5) of the room. The time taken will be the value of x where this is 1, so the correct equation is indeed x/4 + x/5 = 1.

There are numbers on the denominator but not the numerator simply because the time it takes each of them to complete painting the room is a whole number of hours. If Jen could paint it in 3.5 = 7/2 hours, the equation would be 2x/7 + x/5 = 1 instead.

Answer 2

Jen can paint one room in four hours, therefore her rate of work is 1/4 room per hour. Rhonda can paint one room in five hours, therefore her rate of work is 1/5 room per hour. If they combine their efforts, their rate of work is 1/4 + 1/5 or 9/20 rooms per hour. 9/20 rooms per hour times x number of hours equals one room gives you an answer of 20/9 or 2.22 hours. You have simply written it as (1/4 + 1/5)*x = x/4 + x/5 instead of adding the fractions together first. Good luck!

Answer 3

The solution to this type of problem is always product over sum.
So time = 4*5/(4+5) = 20/9 = 2 2/9 hours = 2.222222 hours.

The equation could have been written x/4+x/5 = x/x
Now you have a variable in the denominator.