anonymous
  • anonymous
At the beginning of a walk, Kevin and martin are 3.3 miles apart. If they leave at the same time and walk in the same direction, Kevin overtakes Martin in 11hours. If they walk towards each other, they meet in 1 hour. What are their speeds?
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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anonymous
  • anonymous
Need help with this problem Thnx
phi
  • phi
Let K be Kevin's speed and M be Martin's speed We use Speed x Time = Distance when walking toward each other, they walk for the same amount of time = 1 hour does this make sense K * 1 + M*1 = 3.3 distance of both add up to 3.3 miles
anonymous
  • anonymous
Yes does make sense, I did that so far but couldn't get their speeds

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phi
  • phi
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phi
  • phi
The picture shows Martin with a 3.3 mile head start on Kevin Martin walks for 11 hours. so he walks M*11 miles (using speed * time = distance) In the same 11 hours Kevin catches up with Martin. Kevin walks K*11= 3.3+D so you have 2 equations: 11K= D+3.3 11M= D can you get rid of the D to get one equation with just K and M in it?
anonymous
  • anonymous
I'll try the equation
phi
  • phi
one way is replace D in the first equation with 11M, because D=11M
phi
  • phi
If you do, we now have these 2 equations K + M = 3.3 (when walking toward each other) 11K= 11M+ 3.3 (when walking in the same direction) Do you know how to solve these for K and M?
anonymous
  • anonymous
having problems plugging 11M for distance
phi
  • phi
11K= D+3.3 <--- in this equation replace D with 11M because you know D= 11M 11M= D
anonymous
  • anonymous
I got 11k=14.3
phi
  • phi
You are one of those people who does not like letters. Pay attention: when we say "Add 11M to 3.3" all we can do is write "11M+3.3" we do not ignore the M. we cannot combine the 11 with 3.3 All we can do is write the plus sign. So try again.
anonymous
  • anonymous
11k=11m+3.3
phi
  • phi
Yes. now we have these 2 equations: K + M = 3.3 (when walking toward each other) 11K= 11M+ 3.3 (when walking in the same direction)
phi
  • phi
Now we have to solve those 2 equations. one way is put both K and M parts on the left side. the first equation is ok (both K and M are on the left of the =) do you know how to move the 11M to the left side in the second equation?
anonymous
  • anonymous
Dividing or cancelling out each side by 11?
phi
  • phi
Here is how: 11K = 11M+3.3 now subtract 11M from both sides 11K-11M= 11M+3.3-11M now here is another good rule to know: we can change the order on the right side 11K-11M= 11M-11M+3.3 Here is another good rule: if you have 11M (think M is a thing) and you subtract 11M then you have 0M. Does that make sense?
anonymous
  • anonymous
Yes
phi
  • phi
so what does this simplify into: 11K-11M= 11M-11M+3.3
anonymous
  • anonymous
you can't subtract 11k -11M 2 diff. letters, on the right will be 3.3
phi
  • phi
yes
phi
  • phi
so we now have K+M= 3.3 11K-11M= 3.3 multiply the top equation by 11. That means multiply both sides by 11. And that means multiply every term by 11.
anonymous
  • anonymous
11k+11m=36.3
phi
  • phi
OK now we have 11k+11m=36.3 11k-11m= 3.3 we can add the 2 equations together. Do you know how to do that?
anonymous
  • anonymous
11k+11m=36.3 11k-11m=3.3
phi
  • phi
we can add the 2 equations together. Do you know how to do that?
anonymous
  • anonymous
22k=39.6
phi
  • phi
now solve for k. Divide both sides by 22
anonymous
  • anonymous
1.8miles/hr
phi
  • phi
now go back to one of our equations (always pick the simplest one) K+M= 3.3 replace K with 1.8 solve for M
anonymous
  • anonymous
1.5 miles/hr
phi
  • phi
Yes, you have it! we can check Kevin walks 1.8 miles in 1 hour, and Martin walks 1.5 mile in 1 hour so together they walk 3.3 miles.
phi
  • phi
In 11 hours Martin walks 1.5*11= 16.5 miles. We think Kevin walks 3.3 more or 19.8 Let's check: 1.8*11 = 19.8 miles. So your answer works.
anonymous
  • anonymous
Thanks Phi. Good techer!
phi
  • phi
If you want to see how to solve equations, watch Khan's videos. http://www.khanacademy.org/math/algebra/solving-linear-equations/v/simple-equations He has some on how to do multiple equations like this problem, but first get good at simple equations. I hope I helped.
anonymous
  • anonymous
Yes You did and I'll visit that site.
phi
  • phi
One of many on systems of equations http://www.khanacademy.org/math/algebra/systems-of-eq-and-ineq/v/systems-of-equations

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