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July 17th, 2014, 02:58 AM  #1 
Senior Member Joined: Jan 2012 Posts: 723 Thanks: 7  Find the normal average rate at which Isatu walks to school.
Isatu walks a distance of 1.5km to school everyday; her rate of walking being always constant. On a certain day, owing to ill health, she had to reduce her walking rate by 0.5km/ h and as a result, she took extra 6 minutes to reach the school than usual. Find the normal average rate at which Isatu walks to school. Time t = 6/60=1/10h Let her normal walking rate be x. If she reduce it by 0.5km/h, the walking rate becomes (x0.5)km/h when she was sick. I can't go further here, I need help please. 
July 17th, 2014, 05:27 AM  #2 
Senior Member Joined: Nov 2013 From: Baku Posts: 502 Thanks: 56 Math Focus: Geometry 
Velocity is v, time is t. vt=1.5 and (v0.5)(t+0.1)=1.5 6 min. is 0.1 hours. We get t=(v0.5)/5 and we know t=1.5/v. Rest is easy. Change your profile picture. 
July 17th, 2014, 08:21 AM  #3 
Senior Member Joined: Apr 2014 From: Europa Posts: 571 Thanks: 176 
You forgot change your profile picture. $\displaystyle \color{blue}{Read \ "Decalogue"... \\\;\\ and\ let \ you \ read .}$ 
July 17th, 2014, 11:20 AM  #4  
Senior Member Joined: Jan 2012 Posts: 723 Thanks: 7  Quote:
 
July 17th, 2014, 09:27 PM  #5 
Senior Member Joined: Jan 2012 Posts: 723 Thanks: 7  
July 18th, 2014, 12:41 AM  #6 
Senior Member Joined: Apr 2014 From: Europa Posts: 571 Thanks: 176  
July 18th, 2014, 06:23 AM  #7 
Senior Member Joined: Nov 2013 From: Baku Posts: 502 Thanks: 56 Math Focus: Geometry 
(v0.5)(t+0.1)=1.5 therefor vt+0.1v0.5t0.05=1.5 and we know vt=1.5 therefore 0.1vo.5t0.05=0 therefore v5t0.5=0 and t=1.5/v therefore v7.5/v0.5=0 v^2  0.5v  7.5 = 0 
July 19th, 2014, 09:00 PM  #8  
Senior Member Joined: Jan 2012 Posts: 723 Thanks: 7  Quote:
Using quadratic formula, we will come to a point where we have $\displaystyle \frac{0.5\pm\sqrt{30.25}}{2}$ = $\displaystyle \frac{0.5pm5.5}{2}\rightarrow \\ v=3 \;or 2.5$ So normal rate = $3km/h$ Last edited by Chikis; July 19th, 2014 at 09:19 PM.  
July 19th, 2014, 09:15 PM  #9 
Senior Member Joined: Nov 2013 From: Baku Posts: 502 Thanks: 56 Math Focus: Geometry 
2.5 is also valid solution, if Isatu walks backwards.

July 19th, 2014, 10:22 PM  #10 
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 12,757 Thanks: 860  

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