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I got 11 algebra questions doing rational equations. Please…

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I got 11 algebra questions...
I got 11 algebra questions doing rational equations. Please help.

1. Solve: 3/2+1/3=1/x
2. Solve: 3/5x+8/x=1
3. Solve: 6/x+1=8/x
4. Solve for x: x+3/x+2=x+1/x+3
5. Solve for x: 4/x-3+3/x+3=2x/x^2-9
6. Solve for a:3-a-1/a+2=a^2-1/a+2
7. Solve: (2a-1)=a+7/a+1
8. Solve: Jacks usually mows his lawn in 7 hrs. Marilyn mows the same yard in 5 hrs. how much time would it take for both of them to mow it together?
9. Solve: The speed of a passenger train is 16 mph faster than a freight train.The passenger train travels 280 miles in the same time it takes the freight train to travel 200 miles. What is the speed of each train?
10. A long distance trucker traveled 160 miles in one direction during a snow storm. On the trip back during rainy weather he doubled his speed and took 4 hrs less. What was his speed?
11. A sample of 143 firecrackers contained 9 duds. How many duds would be in a sample of 2860 firecracke3rs?
Submitted: 8 years ago.Category: Math Homework
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Answered in 33 minutes by:
6/11/2010
Math Tutor or Teacher: Emanuel, Bachelor's Degree replied 8 years ago
Emanuel
Emanuel, Bachelor's Degree
Category: Math Homework
Satisfied Customers: 614
Experience: Aerospace engineer, expert in Maths and Physics
Verified
Hello, here are the answers; please check if the parenthesis I added to the equations match what you had in your exercises

1. Solve: (3/2)+(1/3)=(1/x)
9/6+2/6=1/x
11/6=1/x
x=6/11

2. Solve: 3/(5x)+8/x=1
3/(5x)+40/(5x)=1
43/(5x)=1
5x/43=1
x=43/5

3. Solve: (6/x)+1=8/x
1=(8/x)-(6/x)
1=2/x
x/2=1
x=2

4. Solve for x: (x+3)/(x+2)=(x+1)/(x+3)
(x+3)²/[(x+2)(x+3)]=(x+1)(x+2)/[(x+2)(x+3)]
(x²+6x+9-x²-3x-2)/[(x+2)(x+3)]=0
(3x+7)/[(x+2)(x+3)]=0
(3x+7)=0
x=-7/3

5. Solve for x: 4/(x-3)+3/(x+3)=2x/(x²-9)
[4(x+3)+3(x-3)-2x]/(x²-9)=0
(5x+3)/(x²-9)=0
(5x+3)=0
x=-3/5

6. Solve for a: 3-(a-1)/(a+2)=(a²-1)/(a+2)
[3(a+2)-(a-1)-(a²-1)]/(a+2)=0
(-a²+2a+8)/(a+2)=0
(a²-2a-8)/(a+2)=0
a²-2a-8=0
a=1±√(1+8)=1±3
a=4 (a=-2 is not an acceptable solution)

7. Solve: (2a-1)=(a+7)/(a+1)
[(2a-1)(a+1)-(a+7)]/(a+1)=0
(2a²+2a-a-1-a-7)/(a+1)=0
(2a²-8)/(a+1)=0
a²-4=0
a=±2

8. Solve: Jacks usually mows his lawn in 7 hrs. Marilyn mows the same yard in 5 hrs. how much time would it take for both of them to mow it together?
In 1 hour Jack mows 1/7 of the lawn
In 1 hour Marilyn mows 1/5 of the lawn
In 1 hour working together they mow (1/7+1/5)=12/35 of the lawn
Together they would need 35/12 hours to mow the lawn (2+11/12 hours)

9. Solve: The speed of a passenger train is 16 mph faster than a freight train. The passenger train travels 280 miles in the same time it takes the freight train to travel 200 miles. What is the speed of each train?
time=(280-200)/16=5 hours
speed1=200/5=40mph
speed2=280/5=56mph


10. A long distance trucker traveled 160 miles in one direction during a snow storm. On the trip back during rainy weather he doubled his speed and took 4 hrs less. What was his speed?
speed(snow)=20mph
speed(rain)=40mph


11. A sample of 143 firecrackers contained 9 duds. How many duds would be in a sample of 2860 firecracke3rs?
duds=(9/143)*2860=180

Emanuel
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