A bicyclist rode into the country for 5hr. In returning her speed was 5 mi/h faster and the trip took 4 hr. what was her speed each way?
What equation would I use to solve this problem i have no idea
Let V be her speed going out, so V+5 will be her speed coming back. Let the distance each way be D.
L/V = 5 hours
L/(V+5) = 4 hours
Two equations, two unknowns. Solve for V
L= 5 V
L = 4V + 20
Subtract the second equation from the first, and rearrange.
V = 20 mi/h
I saw another tutor work a similar problem this way with a table and I thought it made the problem simper to see how to solve it.
..........rate....time......d=r*t
going......r.......5 hrs....d=r*5
return.....r+5.....4 hrs....d=(r+5)*4
The distance is the same; therefore,
d=d
r*5=(r+5)*4
solve for r.
the d=r*t = 5r.
Post your work if you get stuck.
Geometry.the volume of the boxis represented by (x^2+5x+6)(x+5). find the polynomial that represent the area of the bottom of the box.
Ok Igot this much not sure where to go after this
r*5=(r+5)*4
5r=(r+5)*4
5r=4(r+5)
5r=(4*r)+(4*5)
5r=4r+20
5r-4r=20
r=20
If i am right the the distance is 100 miles
where do I go from here to find the speed each way ?
Read my first answer again. It tells you how to get the speeds. Knowing the distance and the time also lets you computer either speed
DrBob, that was me
I have taught dist-rate-time problems using the chart for over 35 years, there is no better way.
It makes it so easy to see.
The trinomial factors easily into (x+2)(x+3).
So your 3 dimensions of the box obviously are x+2,x+3, and x+5
From the question we cannot tell which are the length width or height.
So the expansion of any two of them could give you the area of the bottom.
To find the polynomial that represents the area of the bottom of the box, you need to expand the given expression (x^2 + 5x + 6)(x + 5).
Using the distributive property, you can multiply each term in the first expression (x^2 + 5x + 6) by each term in the second expression (x + 5).
(x^2 + 5x + 6)(x + 5)
= x(x^2 + 5x + 6) + 5(x^2 + 5x + 6)
= x^3 + 5x^2 + 6x + 5x^2 + 25x + 30
= x^3 + 10x^2 + 31x + 30
Therefore, the polynomial that represents the area of the bottom of the box is x^3 + 10x^2 + 31x + 30.