Algebra Homework Help?

Question

A consultant traveled 9 hours to attend a meeting. The return trip took only 8 hours because the speed was 4 miles per hour faster. What was the consultant's speed each way?

Solve for r. q = 18r

One number is 2 less than another. If 5 times the smaller number minus 2 times the larger number is 14, find the two numbers.

Answer 1

Let x=the speed on the trip to the meeting. Then 9x=8(x+4) since on the way home he went 4 mph faster. Distribution gives 9x=8x+32. Subtract 8x from both sides to get x=32. That means the speed on the way TO the meeting was 32mph. So on the way home it was 36mph.

Divide 18 from both sides...you get r=18/q

Let x=y-2 (x is two less than y). So x is the smaller number. So then you get 5x-2y=14. Substitute y-2 in for x to get 5(y-2)-2y=14. Distribute, you get 5y-10-2y=14. Simplify to get 3y-10=14. Add 10 to both sides you get 3y=24. So y=8. Which means x=6.

Answer 2

Okay. Three questions.

1) You are trying to find the consultant's speed each way. So lets define x as his speed going to attend the meeting, and y as his speed coming back. We need to make a system of equations.
First equation is y = x + 4. His speed coming back is equal to his speed coming down plus 4 mph.
Second equation is 9x=8y, because he traveled the same distance each way.

y = x + 4
9x = 8y
Substitute for y.
9x = 8(x + 4) => 9x = 8x + 32 --> x = 32 (HIS SPEED GOING UP WAS 32 MPH!)
Substitute back in
y = (32) + 4 --> y = 36 (HIS SPEED COMING BACK WAS 36 MPH!)

2)
q = 18r; r
Divide by 18
q/18 = r
Done. r = q/18

3) Smaller number = x, Bigger number = y
x = y - 2
5x - 2y = 14

5(y - 2) - 2y = 14
5y - 10 - 2y = 14
3y = 24
y = 8 (THE BIGGER NUMBER IS 8!)

x = (8) - 2
x = 6 (THE SMALLER NUMBER IS 6!)

Answer 3

I will have to work on the first one, but i do have help for the other two.

Solve for r. q=18r You have to perform the reverse operation that involves the variable you are solving for. In this case the variable is r. Since 18 is multiplied by r, the you must divide q by 18 to find r. The answer is r=q/18.

The next problem has to be set up like this.
Let x=one number
Let x-2=the other

x-2 is the smaller number, so you will multiply this by 5 and then subtract 2x from it and set it equal to 14.

5(x-2) - 2x=14
5x - 10 - 2x=14
3x - 10=14
3x=24
x=8

Since x=8, the x-2=6
8 and 6 are your numbers

Hope this helps a little

Answer 4

First one: 9x = 8 (x+4)
9x = 8x+32
x=32
32 miles per hour there; 36 miles per hour back

Second one: r = 18/q

Third one:
smaller number = x
larger number = y

The two equations are:
5x-2y = 14
y-2 = x

Substitute x in the first equation:
5(y-2)-2y=14
5y-10-2y=14
3y-10=14
3y=24
y=8

x=y-2
x=8-2
x=6

Answer 5

about the consultant question
let speed be x
Distance=speed/time taken
distance when going to the meeting=x/9
Distance on teh return trip=x+4/9
Equatin the equations
x/9=x+4/8
8x=9x+36
x=speed when going to the meeting=36 miles per hour
Speed on the return trip=36+4=40 miles per hour

solving for r when q=18r
divide both sides of the equation by 18 the equation becomes
q/18=r

Answer 6

Hmmm...i gotta think about that one. I'm in Algebra 2 though

Answer 7

IM IN ALGEBRA TOO! but sorry, i dont feel like doing it right now, thats exactly what i just learned too! lol