Problem Solving with Systems...

[helphelphelphelp]

My question: Kareem took 5 hours to drive 470 km from Regina to Medicine Hat. For part of the trip, he drove at 100 km/ h. For the rest of the trip, he drove at 90 km/ h. How far did he drive at each speed?

My problem: This is the only question on the page which is bugging me because: 1. I don't know how to organize the info on a chart because the other questions are simply "find the speed of the boat in still water and the speed of the current [equation one includes ](b + w) [then equation two includes] (b - w)" etc. 2. Because I don't know how to organize the chart, I create a monster of scribbles and sketchings of numbers trying to solve it. For example, one of my attempts is: [first equation] 100X + 90y = 5 [second equation] X + y = 470km [Solve and...] y = 4699.5 x = 422485

Please help asap!

 

[Denis]

[Regina]@100............x miles...........y hours|@90...........470-x miles.........5-y hours[Medicine Hat]

Part 1: x = 100y

Part 2: 470-x = 90(5-y) ; x = 90y + 20

Finish it.

 

[helphelphelphelp]

Ok so if i follow that this is what I got.

1. X = 100 Y

2. 470 - X = 90 (5 - y) 3. 470 - x = 450 - 90y 4. -x + 90 y = -20 5. x - 90y = 20 6. X = 90y + 20 7. (100y) = 90y + 20 8. -10y = -20 9. [ y=2 ]


(follow my steps 1. 2. 3. etc.)

I'm going to stop at step 9. because in my answer book, y does not equal 2. So what did I do wrong?

 

[Denis]

You're sure complicating things! I gave you this:
Part 1: x = 100y
Part 2: 470-x = 90(5-y) ; x = 90y + 20

So 100y = 90y + 20
10y = 20
y = 2 : you sure don't need 9 steps :shock:

That's y = 2 HOURS

Your book would give the distances: that's what is asked for!
So calculate the DISTANCES; 2 hours @?, 3 hours @? : kapish?