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safia21

  • 5 years ago

Ryan drives 10mi/h slower than Maya, And it takes ryan 1 hour longer to travel 300 miles. How long does it take Maya to make a trip

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  1. sandra
    • 5 years ago
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    I'll let amistre get this :p

  2. sandra
    • 5 years ago
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    well, you need two equations and two variables to be able to solve this

  3. sandra
    • 5 years ago
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    one variable is the time it takes Maya to take the trip, and one variable is the time it takes ryan to take the trip

  4. safia21
    • 5 years ago
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    I got 300(x)= 300(x-1) + 10x(x-1)

  5. sandra
    • 5 years ago
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    well, actually, let's make the two variables the speed of each person - then we can easily solve for how long it takes maya to drive 300 miles. So: 1. R = M - 10 2. 300/R - 300/M = 1

  6. anonymous
    • 5 years ago
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    i think i have an answer.

  7. sandra
    • 5 years ago
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    what did you get?

  8. anonymous
    • 5 years ago
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    i got 60 but it was kind of a pain the way i did it. maybe an easier way.

  9. anonymous
    • 5 years ago
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    i used maya's rate as r, ryan's as r - 10 and then \[\frac{300}{r}=\frac{300}{r-10}+1\]

  10. anonymous
    • 5 years ago
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    that is ryan's time is one hour more than maya's.

  11. sandra
    • 5 years ago
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    right. yeah that makes sense

  12. safia21
    • 5 years ago
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    sorry but i do not understand

  13. anonymous
    • 5 years ago
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    i made a mistake somewhere i am trying again.

  14. anonymous
    • 5 years ago
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    first of all the answer: ryan travels at 50 mpr and maya at 60. it is easy to check: \[d=rt\] \[t=\frac{d}{r}\] if maya travels 300 miles at 60 miles an hour she makes the trip in \[\frac{300}{60}=5\] hours while ryan takes \[\frac{300}{50}=6\] hours or one hour longer. so this is the correct answer.

  15. safia21
    • 5 years ago
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    O i understand thank you!

  16. anonymous
    • 5 years ago
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    well i got the correct answer, but i am trying to find the right algebra to solve it for you.

  17. anonymous
    • 5 years ago
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    whew finally. ok here goes. ready?

  18. safia21
    • 5 years ago
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    yes!

  19. anonymous
    • 5 years ago
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    ok we use \[t=\frac{d}{r}\] and we know that ryans rate is r-10 and his maya's time is one less than ryan's. Maya's time is \[\frac{300}{r}\] and ryan's is \[\frac{300}{r-10}\] and \[\frac{300}{r}-1=\frac{300}{r-10}\]

  20. anonymous
    • 5 years ago
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    that says maya's time is one less than ryans. to solve for r, easiest to subtract first on the left hand side: \[\frac{300-r}{r}=\frac{300}{r-10}\] now cross multiply: \[(r-10)(300-r)=300r\] mutiply out \[300r-3000-r^2+10r=300r\] subtract 300r \[-3000 -r^2+10r=0\]

  21. anonymous
    • 5 years ago
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    damn

  22. anonymous
    • 5 years ago
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    thought i had \[(r-60)(r+50)=0\] so r = 60 but i seem to have made another mistake somewhere. i will try to find it.

  23. anonymous
    • 5 years ago
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    oh lord. i put the one on the wrong side! should have been \[\frac{300}{r}+1=\frac{300}{r-10}\]

  24. anonymous
    • 5 years ago
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    maya's time plus one gives ryans time. ok now. \[\frac{300+r}{r}=\frac{300}{r-10}\] \[(300+r)(r-10)=300r\] \[300r -3000+r^2-10r=300r\] \[r^2-10r-300=0\] \[(r-60)(r+50)=0\] \[r=60\] or \[r=-50\] which makes no sense in this problem so \[r=60\] sorry it took a while.

  25. safia21
    • 5 years ago
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    its okay and thanks again

  26. anonymous
    • 5 years ago
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    sorry i made a mistake originally. hope it was not too confusing.

  27. safia21
    • 5 years ago
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    it wasnt thanks

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