when linda and martin work together painting one room, they can complete the work in 5 hours. when linda works alone it takes her 7 hours to paint the same room. how long would it take marvin to paint the room alone?
To find out how long it would take Marvin to paint the room alone, we can first calculate Linda's rate of work. We know that Linda and Martin can complete the work together in 5 hours, so their combined rate of work is 1 room / 5 hours = 1/5 room per hour.
Now, if Linda works alone, it takes her 7 hours to paint the room. We can use this information to find her individual rate of work: 1 room / 7 hours = 1/7 room per hour.
Since we know the combined rate of work when Linda and Martin work together is 1/5 room per hour, and we have Linda's individual rate of work (1/7 room per hour), we can find Martin's individual rate of work by subtracting Linda's rate from the combined rate:
Martin's rate = Combined rate - Linda's rate = 1/5 - 1/7 = (7/35) - (5/35) = 2/35 room per hour.
Now that we know Martin's rate of work is 2/35 room per hour, we can calculate the time it would take him to paint the room alone by taking the reciprocal of his rate:
Time for Martin to paint the room alone = 1 / (2/35) = 35/2 = 17.5 hours.
Therefore, it would take Marvin approximately 17.5 hours to paint the room alone.
linda --- 1 room/7 hours
marvin ---- 1 room/x hours
5 hours (1/7 + 1/x) = 1
1/7 + 1/x = 1/5
multiply all terms by 35 x
5 x + 35 = 7x
2 x = 35
x = 17.5 hours