Question

plse help me solve this sum
sum no. 16

Answer 1

http://books.google.co.in/books?id=Hk2pJOtKNs8C&pg=PA182&lpg=PA182&dq=A+horse+can+walk+at+a+speed+of+9+km/hr+and+can+trot+at+a+speed+of&source=bl&ots=uHfzh8dN9J&sig=BdQEaYKiWsmkX-UxUx_90igSu4c&hl=en&sa=X&ei=xPW6UeqjOoXsrAeJ34DgAQ&ved=0CFUQ6AEwBw#v=onepage&q=A%20horse%20can%20walk%20at%20a%20speed%20of%209%20km%2Fhr%20and%20can%20trot%20at%20a%20speed%20of&f=false

Answer 2

Okay, let x be the time (in hours) that it walked and y be the time (in hours) that it trotted.
Then you have
9x + 15y = 11

Answer 3

Where x and y are both between 0 and 1.

This is about as far as I can go...

Answer 4

oh yeah, sorry,
x + y = 1

and you have a system :D

Answer 5

9x + 15y = 11
x + y = 1

And just solve for x and y :)

Answer 6

okay

Answer 7

y=1/3
x=2/3

Answer 8

no that's not it :D

Answer 9

Let's work with the second equation first....
x + y = 1

Now, let's subtract x from both sides to yield
y = 1 - x

You now have an expression of y in terms of x.

So what you do is replace the y in the first equation
9x + 15y = 11

with 1 - x

and then solve for x.

Answer 10

yes, x= 2/3 and y = 1/3 is coming

Answer 11

oh sorry, I misread your first post of your answer as
x = 1/3
and
y = 2/3

Good job... sorry for the mix-up T.T

Answer 12

@amistre64
i need ur help

Answer 13

huh? you've already solved it, haven't you?

Answer 14

i cant see the details of the question. the link is a book cover

Answer 15

Second response was a question though :D

Answer 16

9x + 15y = 11, find the gcd(9,15)

Answer 17

i believe its 3

9x + 15y = 3 can be solved.

15 = 9(1) + 6
9 = 6(1) + 3 <-- gcd = 3
6 = 3(2) ...

0
0 1
0-1(1) = -1
1-1(-1) = 2 ; x= 2

9(2) + 15(-1) = 3 and y = -1

multiply it all by 11/3

9(22/3) + 15(-11/3) = 11

this gives us something to work with that may be useful

Answer 18

With permission amistre-sensei (^.^)

If it covered 11 kilometers in one hour, then the time it takes trotting and walking together should add up to one hour, right?

So consider
x + y = 1
and make a system.

Answer 19

9km/hr * n hrs = 9n km

since we are looking for 11 km traveled, and what times were troted and sleeping ....

Answer 20

of course this is just an idea i have :)

Answer 21

thanks to euler

x = 22/3 + 5n
y = -11/3 - 3n

would accomodate us

and i just got your concern yes, x+y add up to an hour

Answer 22

so our limits for n are such that 0 <= x,y <= 1

Answer 23

22/3 + 5n > 0 ; n> -22/15
22/3 + 5n < 1 ; n< -19/15


y = -11/3 - 3n >0 ; n < -11/9
y = -11/3 - 3n <1 ; n > 2/9

the union of these 2 sets should define all the n parts that would work. with any luck :)

Answer 24

y = -11/3 - 3n >0 ; n < -11/9
y = -11/3 - 3n <1 ; n > -20/9

looks better me thinks

Answer 25

Why can't we just solve the system? T.T

Answer 26

you can if you want too, but i really dont need the practice doing it that way ;)

Answer 27

I see.
<bows to sensei>
(^.^)

Answer 28

Yeah :P
That was the gist of it :)

We were looking for x (the number of hours the horse walked)
and you got 2/3.

So that's 2/3 hours
which is exactly 40 minutes.

Now as to how far the horse walked, the horse walked 9km/hr
so just multiply that to 2/3, and you'll get the distance traveled.

2/3 of 9 is 6 (km)

There ya go :P

Answer 29

22/3 + 5n > 0
5n > -22/3
n > -22/15

22/3 + 5n < 1
5n < 1 - 22/3
n < 1/5 - 22/15
n < -19/15


-11/3 - 3n >0
- 3n > 11/3
n < -11/9

-11/3 - 3n <1
- 3n <1 + 11/3
n > -1/3 - 11/9
n > -14/9

lcm(9,15) = 45


-66/45 < n < -57/45
-70/45 < n < -55/45

looks like (-66/45, -57/45) is the interval for n to me

Answer 30

x = 22/3 + 5(-66/45)
x = 66/9 -66/9 = 0

y = -11/3 - 3(-66/45)
y = -55/15 + 66/15 = 11/15

9(0) + 15(11/15) = 11



x = 22/3 + 5(-57/45)
x = 66/9 -57/9 = 1

y = -11/3 - 3(-57/45)
y = -55/15 + 57/15 = 2/15

9(1) + 15(2/15) = 11

Answer 31

i know somethings amiss in it, but that was fun to try :)

Answer 32

'Tis the realm of the gods :D

Answer 33

hmmm, since x+y = 1 i could have done

22/3 + 5n -11/3 - 3n = 1

11/3 +2n = 1

2n = 1 - 11/3

n = -8/6 = -4/3


x = 22/3 +5(-4/3)
= 22/3 - 20/3 = 2/3 , with any luck that means y = 1/3

y = -11/3 -3(-4/3)
= -11/3 +12/3 = 1/3

:)