1. ## Speed Problem

Fred cycled from home to his friend's house and back again. The distance between their houes is 20km. On his way to his firend's house, Fred cycled at x km/h. On the back, Fred cycled 2 km/h slower. It took Fred 4 Hours altogether to cycle to his friends house and back.

a) write down an equation for x
b) show that the equation can be written as x2 - 12x + 10 = 0

really appreciate the help its driving me crazy!

2. Distance = Rate * Time

Rule #1 - Name Stuff.

The only thing missing in this problem is the time it took to do ONE of the trips. Name that.

y hrs = Time to make the trip to his friend's house at x km/h.

This makes (4 hrs - y hrs) the time it took to make the return trip.

Trip To

Distance = Rate * Time
(20 km) = (x km/h) * (y hrs)

Trip Back

Distance = Rate * Time
(20 km) = (x km/h - 2 km/h) * (4 hrs - y hrs)

We are tasked with writing an equation for 'x'. This requires us to get rid of the 'y's. Solve and substitute.

Trip To (Solve for y)

(20 km) / (x km/h) = (y hrs)

Trip From (Substitute)

(20 km) = (x km/h - 2 km/h) * (4 hrs - ((20 km) / (x km/h)))

And thus we see an equation for 'x'. It isn't real pretty, but it is done. It isn't real pretty, and that's why we have Part B of the problem statement.

Let's see if you can get it from here.

P.S. Don't forget "Distance = Rate * Time"

3. i must be missing something or maybe my brain isnt back from holiday... but i cant quite understand what you've done!

if you could brake it down even more it might help me. thanks soooo much!

4. Really, I think it cannot be broken down any more than that. Maybe the notation is confusing because you are not familiar with it? You should be familiar with the algebraic manipulation (solving for one variable or the other - substitution). If you are not, it would cause me to question if you are in the right course. Perhaps the units all over the place cause you to balk at the dizzying display of notation? Admittedly, there is a lot more going on visually when the units are included. Including the units is important. It will save you many headaches later on. I suggest you get used to it if that is the impediment. It will take practice.

Go one line at a time. Tell me what you get out of each line. Let's see where you are wondering off.