calculusxy
  • calculusxy
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?
Mathematics
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SOLVED
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chestercat
  • chestercat
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calculusxy
  • calculusxy
@jim_thompson5910
calculusxy
  • calculusxy
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.
calculusxy
  • calculusxy
\[\frac{ 12 }{ 60 } = \frac{ 1km }{ 5minutes }\] \[\frac{ 20 }{ 60 } = \frac{ 1 km }{ 3 minute }\]

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More answers

ybarrap
  • ybarrap
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
calculusxy
  • calculusxy
So I I just use your formula then I will get it correct?
calculusxy
  • calculusxy
12t + 1/5 = 20t 12t - 12t + 1/5 = 20t - 12t 1/5 = 8t 1/5 / 8 = 8t / 8 1/40 = t
jim_thompson5910
  • jim_thompson5910
looks good, now plug that into either side of the original equation to find the distance 20t is the easier side
calculusxy
  • calculusxy
20/40 = 1/2 Okay thanks :)
calculusxy
  • calculusxy
But how did @ybarrap make that equation?
jim_thompson5910
  • jim_thompson5910
he used d = r*t d = distance r = rate t = time
calculusxy
  • calculusxy
Also, we are learning about the method called "Backsolving" so if you can help me with that on this problem.
jim_thompson5910
  • jim_thompson5910
on the left side r = 12 t is t+1/60 on the right side r = 20 t is just itself: t
jim_thompson5910
  • jim_thompson5910
|dw:1436397192770:dw|
jim_thompson5910
  • jim_thompson5910
|dw:1436397210345:dw|
jim_thompson5910
  • jim_thompson5910
|dw:1436397232035:dw|
calculusxy
  • calculusxy
So since she is a minute slower, we have to add the 1 right?
jim_thompson5910
  • jim_thompson5910
add 1/60 hrs
jim_thompson5910
  • jim_thompson5910
time is converted to hours because the speeds are in km/hr
calculusxy
  • calculusxy
Oh I am sorry.
jim_thompson5910
  • jim_thompson5910
thats fine
ybarrap
  • ybarrap
Sorry had to leave @calculusxy, loved your questions to this problem! Thanks @jim_thompson5910 for following-up!

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