1.A father can do a job in a certain number of hours. His son takes twice as long to do the job. Working together, they can do the job in 6 hours. How many hours does it take the father to do the job alone?
A.9
B.18
C.12
D.10
3.David is 5 years older than Paul. In 5 years, David will be twice as old as Paul is now. How old is David now?
A.15
B.10
C.25
D.20
this is what i have so far:
D=p+5
2D+p(i'm not sure if this is right)
1.
combined rate=1/F +.5/F=1.5/F=1/6
f=9 hrs
D-5=P
D+5=2P
subtract second equation from first
-10=-P P is 10 now, so D is 15
job/rate = time --> rate = job/time
let the fathers rate = job/x
let the son's rate be job/2x
combined rate =job/x + job/2x
= 3job/(2x)
combined time = job ÷(3job/2x)
= job (2x/3job)
= 2x/3
but 2x/3 = 6
2x = 18
x = 9
It would take 9 hrs for the father to work alone
3.
Paul's age --- x
David's age -- x+5
in 5 years:
David --> x+10
x+10 = 2x
x = 10
Paul is now 10 and David is now 15
To solve these problems, we can set up equations based on the given information.
1. Let's say the father takes x hours to do the job alone. Since his son takes twice as long, we can say the son takes 2x hours to do the job alone.
Working together, they can do the job in 6 hours, so their combined work rate is 1/6 of the job per hour.
The father's work rate is 1/x of the job per hour, and the son's work rate is 1/(2x) of the job per hour.
Using the work rate formula: work rate = amount of work done / time taken
We can set up the equation: 1/x + 1/(2x) = 1/6
To solve this equation, we can multiply through by the least common multiple of the denominators, which is 6x.
6 + 3 = x
Simplifying, we get x = 9.
Therefore, it takes the father 9 hours to do the job alone. So the answer is A. 9.
3. Let's say Paul's current age is x.
According to the given information, David is 5 years older than Paul, so David's current age is x + 5.
In 5 years, David will be x + 5 + 5 = x + 10 years old.
The problem also states that in 5 years, David will be twice as old as Paul is now.
So we can set up the equation: x + 10 = 2x
Simplifying, we get x = 10.
Therefore, Paul's current age is 10. Since David is 5 years older, his current age is 10 + 5 = 15.
So the answer is D. 15.