Algebra word problem

Question

Janet jogged for 10 miles and then cycled for another 45.5 miles. Her cycling speed was 6 miles per hour faster than her jogging speed. If her total time for jogging and cycling was 4.5 hours at what rate did she cycle?

 

 

Answer 1

Time spent walking = t_w = 10/x 

Time spent cycling = t_c = 45.5/(x+6)

 

t_w + t_c = 10/x + 45.5/(x+6) = 4.5 hrs

 

10(x+6) + 45.5x = 4.5 (x² + 6x)

55.5x + 60 = 4.5x² + 27x

-4.5x² + 28.5x + 60 = 0

 

using the quadratic formula

 

x = {-28.5 ±√[28.5² - (4)(-4.5)(60)]}/2(-4.5)

= [-28.5 ±√(812.25 + 1080)]/-9

  = (-28.5 ± 43.5)/-9

 

since we are not interested in negative speeds we will evaluate -72/-9 = 8 mph is her walking speed and 8 + 6 = 14 mph is her cycling speed.

 

verify 10/8 + 48.5/14 = 1.25 + 3.25 = 4.5 hrs.