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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. Write and solve
a system of equations to find the
painting speed of each person,
in square meters per hour. Then
calculate how long it would take
Hal and Ula to paint 90 square
meters of wall together.

User Jelgab
by
6.7k points

1 Answer

7 votes

Final answer:

To determine the painting speeds of Hal and Ula, set up a system of linear equations using the given information. Solve the system to find individual speeds, then calculate the combined time it would take for them to paint 90 square meters together.

Step-by-step explanation:

To find the painting speed of Hal and Ula, we can set up a system of linear equations based on the information given. Let's denote Hal's painting speed as H and Ula's painting speed as U, both in square meters per hour.

From the first part of the problem, we know that together they paint 30 square meters in 1 hour. This can be written as the equation:

  1. H + U = 30

From the second part of the problem, we have that Hal works for 30 minutes (0.5 hours) and Ula works for 45 minutes (0.75 hours) to paint another 18 square meters. This gives us the second equation:

  1. 0.5H + 0.75U = 18

Solving this system of equations, we can find the individual painting speeds of Hal and Ula.

Once we have found H and U, we can calculate how long it would take them to paint 90 square meters together. Since they work at a combined rate of H + U square meters per hour, we can use the equation:

  1. 90 / (H + U) = Time to paint 90 sq m together

By substituting the values of H and U, we get the time it would take them to complete the 90 square meter wall.

User Jeff Hernandez
by
7.8k points