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?

Question

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.