Together, Hal and Ula paint 30 square meters of a wall in
1 hour. Then they paint another
18 square meters, but Hal works for 30 minutes while Ula works for 45 minutes.
Part A
Find the painting speed of each person, in square meters per hour.
Hal:
Ula:
Part B
How many hours would take Hal and Ula to paint 90 square meters of wall together?
Part A:
Let H be Hal's painting speed in square meters per hour and U be Ula's painting speed in square meters per hour.
Given that Hal and Ula together paint 30 square meters in 1 hour:
H + U = 30
Hal then paints another 18 square meters in 30 minutes (0.5 hours) while Ula paints another 18 square meters in 45 minutes (0.75 hours):
0.5H + 0.75U = 18
Solving these two equations simultaneously:
H + U = 30
0.5H + 0.75U = 18
Multiplying the first equation by 0.5 and subtracting it from the second equation:
0.5H + 0.75U - 0.5H - 0.5U = 18 - 15
0.25U = 3
U = 12
Substitute U back into the first equation:
H + 12 = 30
H = 18
Therefore, Hal's painting speed is 18 square meters per hour and Ula's painting speed is 12 square meters per hour.
Part B:
Hal and Ula together paint 30 square meters in 1 hour, so their combined painting speed per hour is 30 square meters.
To paint 90 square meters:
Hal and Ula together would take 90 / 30 = 3 hours.
Therefore, it would take Hal and Ula 3 hours to paint 90 square meters of wall together.