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calculusxy

  • one year ago

In a race, Alice and Brenda started at the same time and ran with constant spends of 12 km and 20 km per hour, respectively. If Alice crossed the finish line 1 minute after Brenda, how many kilometers long was the race?

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  1. calculusxy
    • one year ago
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    @jim_thompson5910

  2. calculusxy
    • one year ago
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    Since it said "minute" somewhere in the problem, I thought of converting the 12km/hr and 20km/hr into minutes. But I am not sure if that's how I am supposed to start it or if that's even correct.

  3. calculusxy
    • one year ago
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    \[\frac{ 12 }{ 60 } = \frac{ 1km }{ 5minutes }\] \[\frac{ 20 }{ 60 } = \frac{ 1 km }{ 3 minute }\]

  4. ybarrap
    • one year ago
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    A minute is 1/60 hr, right? So $$ (t+1/60)12=20t $$ Solve for t then plug back in to find the total distance t is in hours Does this make sense

  5. calculusxy
    • one year ago
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    So I I just use your formula then I will get it correct?

  6. calculusxy
    • one year ago
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    12t + 1/5 = 20t 12t - 12t + 1/5 = 20t - 12t 1/5 = 8t 1/5 / 8 = 8t / 8 1/40 = t

  7. jim_thompson5910
    • one year ago
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    looks good, now plug that into either side of the original equation to find the distance 20t is the easier side

  8. calculusxy
    • one year ago
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    20/40 = 1/2 Okay thanks :)

  9. calculusxy
    • one year ago
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    But how did @ybarrap make that equation?

  10. jim_thompson5910
    • one year ago
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    he used d = r*t d = distance r = rate t = time

  11. calculusxy
    • one year ago
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    Also, we are learning about the method called "Backsolving" so if you can help me with that on this problem.

  12. jim_thompson5910
    • one year ago
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    on the left side r = 12 t is t+1/60 on the right side r = 20 t is just itself: t

  13. jim_thompson5910
    • one year ago
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    |dw:1436397192770:dw|

  14. jim_thompson5910
    • one year ago
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    |dw:1436397210345:dw|

  15. jim_thompson5910
    • one year ago
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    |dw:1436397232035:dw|

  16. calculusxy
    • one year ago
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    So since she is a minute slower, we have to add the 1 right?

  17. jim_thompson5910
    • one year ago
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    add 1/60 hrs

  18. jim_thompson5910
    • one year ago
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    time is converted to hours because the speeds are in km/hr

  19. calculusxy
    • one year ago
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    Oh I am sorry.

  20. jim_thompson5910
    • one year ago
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    thats fine

  21. ybarrap
    • one year ago
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    Sorry had to leave @calculusxy, loved your questions to this problem! Thanks @jim_thompson5910 for following-up!

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