Lisa, Beth, and Tim painted their grandparent's house.
• The amount of time Lisa painted can be represented by x.
• The amount of time Beth painted is 1
3
5
times the amount Lisa painted
• The amount of time Tim painted is 1
2
3
times the amount Lisa painted.
• The total amount of time Lisa, Beth, and Tim painted is 24 hours.
What is x, the amount of time painted by Lisa?
Confused by your 1
3
5 and
1
2
3.
If those are fractions, they need to be printed 1 3/5 and 1 2/3. Is that what you meant?
If so, then you know that
x + (1 3/5)x + (1 2/3)x = 24
Now, 1 3/5 + 1 2/3 = 8/5 + 5/3 = 24/15 + 25/15 = 49/15
so, now you know that
x + 49/15 x = 24
64/15 x = 24
x = 24 * 15/64 = 45/8 = 5 5/8 hours
To solve this problem, we need to set up equations based on the given information and then solve them.
Let's start by assigning variables to each person's painting time:
- Lisa's painting time: x hours
- Beth's painting time: 1/35x (since Beth painted 1/35 times the amount Lisa painted)
- Tim's painting time: 1/23x (since Tim painted 1/23 times the amount Lisa painted)
The total amount of time Lisa, Beth, and Tim painted is given as 24 hours, so we can set up the equation:
x + 1/35x + 1/23x = 24
To solve this equation, we need to find a common denominator for the fractions. In this case, 35 and 23 share the common denominator of 805. Multiplying each fraction by its corresponding denominator, we get:
(805/805)x + (23/805)x + (35/805)x = 24
Simplifying the equation gives us:
(863/805)x = 24
To isolate x, we divide both sides of the equation by (863/805):
x = 24 / (863/805)
Now, we can calculate the value of x:
x = 24 * (805/863)
x ≈ 22.535
Therefore, the amount of time Lisa painted (x) is approximately 22.535 hours.