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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?
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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calculusxy
 one year ago
Best ResponseYou've already chosen the best response.0Since 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
 one year ago
Best ResponseYou've already chosen the best response.0\[\frac{ 12 }{ 60 } = \frac{ 1km }{ 5minutes }\] \[\frac{ 20 }{ 60 } = \frac{ 1 km }{ 3 minute }\]

ybarrap
 one year ago
Best ResponseYou've already chosen the best response.1A 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
 one year ago
Best ResponseYou've already chosen the best response.0So I I just use your formula then I will get it correct?

calculusxy
 one year ago
Best ResponseYou've already chosen the best response.012t + 1/5 = 20t 12t  12t + 1/5 = 20t  12t 1/5 = 8t 1/5 / 8 = 8t / 8 1/40 = t

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.2looks good, now plug that into either side of the original equation to find the distance 20t is the easier side

calculusxy
 one year ago
Best ResponseYou've already chosen the best response.020/40 = 1/2 Okay thanks :)

calculusxy
 one year ago
Best ResponseYou've already chosen the best response.0But how did @ybarrap make that equation?

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.2he used d = r*t d = distance r = rate t = time

calculusxy
 one year ago
Best ResponseYou've already chosen the best response.0Also, we are learning about the method called "Backsolving" so if you can help me with that on this problem.

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.2on the left side r = 12 t is t+1/60 on the right side r = 20 t is just itself: t

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.2dw:1436397192770:dw

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.2dw:1436397210345:dw

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.2dw:1436397232035:dw

calculusxy
 one year ago
Best ResponseYou've already chosen the best response.0So since she is a minute slower, we have to add the 1 right?

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.2time is converted to hours because the speeds are in km/hr

ybarrap
 one year ago
Best ResponseYou've already chosen the best response.1Sorry had to leave @calculusxy, loved your questions to this problem! Thanks @jim_thompson5910 for followingup!
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