Person A can paint the neighbor's house 2 times as fast as Person B. The year A and B worked together, it took them 5 days. How long would it take each to paint the house? So, i know how to setup the problem, but i'm not sure what steps I need to take to solve. This is what I have currently. 1/a+1/b=1/t (t represents time) 132=rt/132=(r+11)(t-2) so t-132/r how do I solve for t? Any help or direction to help would be extremely appreciated, thank you.
I posted the wrong problem for my work provided, although I am struggling to answer both. The correct problem for my work provided is as follows. A car Traveled 132mi at a certain speed. If the speed had been 11mph faster, the trip could have been made in 2hr less time. Find the speed.
This is what I have so far for the paint problem. A+B=5 , A=Bx2
again I know know what steps need to be taken to solve.
If it takes A x days, it takes B 2x days.
1/x + 1/(2x) = 1/5
3/(2x) = 1/5
x = 15/2
So, it takes B 15/2 days, and A 15/4 days
since time = distance/speed,
132/(x+11) = 132/x - 2
x = 22
6 hrs at 22 mph
4 hrs at 33 mph
Thank you Steve.
To solve for the time it would take each person to paint the house, we can follow these steps:
1. Let's assume that Person B takes t days to paint the house. Since Person A can paint the house 2 times faster than Person B, Person A would take t/2 days to paint the house.
2. When A and B work together, it takes them 5 days to paint the house. Using the formula you provided, 1/a + 1/b = 1/t, we can substitute the values:
1/(t/2) + 1/t = 1/5
Simplifying this equation, we get:
2/t + 1/t = 1/5
3. Combining the fractions, we get:
(2 + 1)/t = 1/5
3/t = 1/5
4. Cross-multiplying, we find:
3 * 5 = 1 * t
15 = t
So, it would take Person B 15 days to paint the house alone.
5. To find out how long it would take Person A to paint the house alone, we can substitute the value of t into the equation:
t/2 = 15/2 = 7.5
Therefore, it would take Person A 7.5 days to paint the house alone.
In summary, Person B would take 15 days, and Person A would take 7.5 days to paint the house by themselves.