Peter painted 1/3 of a room while Joe painted 2/5 of the same room. It then took Peter 1 hour, 40 minutes to finish painting the remainder of the room by himself. In how many hours could Peter have painted the entire room by himself? Express answer as a mixed number.
The fraction of the room still to be painted after the two sessions
= 1 - 1/3 - 2/5 = 4/15
so 4/15 or room took 1 hr 40 min or 5/3 hour
so 1 room took (5/3)(15/4) hours or 6.25 hours
or 6 hours and 15 minutes.
mixed number: 6 1/4 hours.
post it.
To find the answer, we can add up the fractions of the room that Peter and Joe painted individually.
Peter painted 1/3 of the room.
Joe painted 2/5 of the room.
To find the total fraction of the room that was painted, we need to find a common denominator for 3 and 5, which is 15.
Then, we can convert the fractions to have the same denominator:
(1/3) * (5/5) = 5/15
(2/5) * (3/3) = 6/15
Now, we can add the fractions together:
5/15 + 6/15 = 11/15
So, Peter and Joe together painted 11/15 of the room.
To find out how much time it would take for Peter to paint the remaining 4/15 of the room by himself, we can set up a proportion:
(1 hour, 40 minutes) / (11/15) = (x hours) / (4/15)
To simplify the calculation, let's convert 1 hour, 40 minutes to an equivalent fraction of hours. There are 60 minutes in an hour, so:
1 hour, 40 minutes = 1 + (40/60) = 1 + (2/3) = 3/3 + 2/3 = 5/3
Now, we can solve the proportion:
(5/3 hours) / (11/15) = (x hours) / (4/15)
To solve for x, we can multiply both sides of the equation by (4/15):
x = (5/3 hours) * (4/15) / (11/15)
x = (20/45) / (11/15) [Multiplying fractions.]
To simplify the calculation, we can divide both the numerator and denominator by the greatest common divisor, which is 5:
x = (4/9) / (11/15)
x = (4/9) * (15/11) [Inverting the second fraction and multiplying.]
Now, we can multiply the numerators and denominators:
x = (4 * 15) / (9 * 11)
x = 60 / 99
To express this as a mixed number, we divide 60 by 99:
60 ÷ 99 = 0 remainder 60
So, the mixed number is 0 and 60/99.
However, we can simplify this fraction by dividing both the numerator and denominator by their greatest common divisor, which is 3:
(60 ÷ 3) ÷ (99 ÷ 3) = 20 ÷ 33
So, the final answer is 0 and 20/33.
Therefore, Peter could have painted the entire room by himself in 0 hours and 20/33 hours, or 0 hours and approximately 36 minutes.