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A cyclist rides 30 km at an average speed of 9 km per hour. At what rate must the cyclist cover in the next 20 km in order to bring the overall average speed up to 10 km per hour?

 Feb 14, 2022
 #1
avatar+36434 
+1

30 km / 9 km / hr =   10 / 3  hr

 

 

(30 km + 20 km )   = 50 km       50 km / 10km/hr = 5 hours

 

5 - 10/3 =   5/ 3 hr   to cover 20 km

 

20 km / 5/3 hr =   12 km / hr

 Feb 14, 2022
 #2
avatar+124594 
+1

The time  for the cyclist  to  ride the first segment  is    30 km / (9km / hr) = 30/9 hr = 10/3 hr

 

Call the  rate that the cyclist must average in the second segment = R

 

The total time for the second segment =  20  km / R km / hr   =  (20/R) hr

 

The total distance traveled =   50 km

 

So

 

Total Distance  / ( Total Time  ) =   Avg  Rate

 

So

 

50  /(10/3  + 20/R)  =  10

 

50 /  10  =   (10/3 + 20/R)

 

5 = 10/3 + 20/R

 

5 - 10/3  = 20/R

 

5/3 = 20 / R

 

R = 20 / (5/3)  =  20 * 3/5  =    60 / 5   =   12 km/ hr 

 

 

cool cool cool

 Feb 14, 2022

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