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I have a map of Iowa on a Cartesian coordinate plane, where one unit represents approximately one minute of travel time. Des Moines is at the origin (0,0). Ames is at (0,30) . Iowa City is at (120,0) . Cedar Rapids is at (120,30) . How much farther is it from Iowa City to Ames than it is from Iowa City to Cedar Rapids? Express your answer in the form $a\pm b\sqrt{c}$ , where a and b are integers.
 

 Sep 4, 2018
 #1
avatar+98128 
+2

Distance  Iowa City to Ames  = √ [ (120^2 + 30^2  ] = √15300 minutes  =  30√17 minutes

 

Distance  Iowa City to Cedar Rapides  =√ [(120 - 120)^2  + 30^2 ]  = √900  =  30 minutes

 

So...the difference in distance is  :   30√17 - 30  minutes  =   -30 + 30√17 minutes

 

 

cool cool cool

 Sep 4, 2018
 #2
avatar+67 
+2

thanks CPhill

 Sep 4, 2018

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