can someone please show me how to do this math?

Question

the road was rocky , so after running for a while at 10 kilometers per hour, Clytemnestra slowed to a 5-kilometer-per-hour walk. if the total trip was 65 kilometers and she made it in 9 hours, how far did she walk and how far did she run?

Answer 1

4 hours of 10kph
5 hours of 5kph

Let x = hours of running, and y = hours of walking.

10x + 5y = 65.
x + y = 9

Now you approach it a bunch of ways. I'll show you what I think is the easiest.

x + y = 9
x = 9 - y

10(9-y) + 5 y = 65 Substitution
90 - 10y + 5y = 65 Multiply both #s in parenthesis by 10.
90 = 65 + 5y Move the y's to the other side, so theyre positive.
25 = 5y Subtract 65 from both sides.
y = 5 Divide both sides by 5.

So five hours of walking. Since she traveled 9 hours, that leaves four hours of running. (Or, you could do another system, but that's more work than necessary.)

Answer 2

It's two equations in two variables.
So, you have 10x + 5y = 65 kilometers, where x and y are the times spent at each speed.
The second equation is x + y = 9, the total time traveled.
If you multiply the second equation by 5, you get:
5x + 5x = 45.
You can now subtract this from the first equation to get:
5x = 20 and you know x is 4.
Now, put 4 for x in the second equation to find 4 + y = 9.
And you know that y is 5.
To double check, put your answers into the first equation and see if it checks out.
10 x + 5y = 65?
(10 * 4) + (5*5) = 65?
40 + 25 = 65? Yep, it checks out.

Answer 3

Hi,

Let's say she ran for x hours. That means the rest of the time, which is 9 - x hours, she was walking. If we multiply her rates by the time she ran and walked, it gives the equation:

10x + 5(9 - x) = 65

Distributing you get:

10x + 45 - 5x = 65

solving this we get:

5x + 45 = 65

5x = 20

x = 4

So Clytemnestra ran for 4 hours and walked for 9-4 or 5 hours. This makes sense because 4 times 10 is 40 and 5 times 5 is 25 more for the total of 65 kilometers.

I hope that helps.

Answer 4

this is a system of equations.
You know that the hours spent walking and running together equal nine, so:
First of all, x + y = 9
You also know that the rate times the time equals the distance so:
secondly, 10x + 5y = 65
so, to solve you can either subtract or substitute.
If you were to substitute, you would plug in x= 9 - y, after having gotten x alone for the x in the second equation.
It would then read 10(9-y) + 5y = 65
Simplified, 90 - 5y = 65
or 5y= 25
I'm sure you can solve from there

Answer 5

x = hours running
y = hours walking

Given:
10x +5y = 65
x + y = 9

Simplify:
x + y = 9
y = 9 -x

Substitute to find x:
10x +5y = 65
10x +5(9 -x) = 65
10x + 45 -5x = 65
5x = 20
x = 4 hours running

Find y:
x + y = 9
4 + y = 9
y = 5 hours walking

Distance running = 10x = 10(4) = 40km
Distance walking = 5y = 5(5) = 25km

Answer 6

Since distance = [distance / time] * time, time = distance / [distance/time].

remember that speed = [distance / time].

If she ran r kilometers and walked w kilometers, then

9 h = r [km] / 10 [km / h] + w [km] / 5 [km / h]
65 km = r [km] + w [km]

w = 65 - r

9 = r / 10 + (65-r) / 5
90 = r + 2(65-r)
90 = r + 130 - 2r
90 = 130 - r

r = 130 - 90 = 40 km
w = 65 - 40 = 25 km

Answer 7

x = distance running
So 65-x = distance running
x/10+(65-x)/5 = 9
x+130 -2x =90
-x=-40
x=40 km = distance running
65-x = 25 km = distance walking

Answer 8

4 hours running and 5 hours walking

Answer 9

10x+5y=65
x+y=9
x=4 and y = 5

Answer 10

jaesus. i know you're a chick, and as such, you don't need to be good at math to get laid, but come on.. try, just try and prove me wrong. by doing it yourself.