Problema Solution
It takes john 75 min to paint a room. It takes Jeff 60 min and Jackie 80 min each to paint the same room. How long will the painting take if all three work together?
Answer provided by our tutors
John paints at a rate of 1 room / 75 min
Jeff paints at a rate of 1 room / 60 min
Jackie paints at a rate of 1 room / 80 min
Therefore, think of time (t) as the number of minutes. For example, if t = 75 min, then John would be finished the room: 1 room / 75 min * 75 min = 1 room
So we need to take all their rates multipled by 't', set the equation equal to 1 and then solve for time:
t/75 + t/60 + t/80 = 1
Simplify the fractions:
17t/400 = 1
Solve for t:
17t = 400
t = 23.53 minutes
So it takes all three of them approximately 23.53 minutes to finish 1 room.