Stu trained for a triathlon for 5 hours yesterday. He ran 5 miles and then biked 80 miles. His biking speed is 15 mph faster than his running speed. What is his running speed?

Answer:Step-by-step explanation:Given as :The distance cover while running = [tex]D_1[/tex] = 5 milesLet The speed for running = [tex]S_1[/tex]The distance cover with bike = [tex]D_2[/tex] = 80 milesThe speed for biking = [tex]S_2[/tex] = 15 mph +  [tex]S_1[/tex]Total Time taken = 5 hoursNow Time = [tex]\dfrac{\textrm Distance}{\textrm Speed}[/tex]∴ 5 hour = [tex]\frac{D_1}{S_1}[/tex] +  [tex]\frac{D_2}{S_2}[/tex]Or,  5 hour = [tex]\frac{5}{S_1}[/tex] +  [tex]\frac{80}{15+S_1}[/tex]Or, 5 hour = [tex]\frac{75 + 5 S_1 + 80 S_1}{S_1(15+S_1)}[/tex]or,  5 × ([tex]S_1^{2}+15 S_1[/tex]) = [tex]85 S_1 + 75[/tex]Or, [tex]5 S_1^{2} + 75 S_1 [/tex] -  [tex]85 S_1 - 75[/tex] = 0or, [tex]5 S_1^{2} -10 S_1 - 75[/tex] = 0or,   [tex] S_1^{2} -2 S_1 - 15[/tex] = 0Or, [tex]S_1^{2} -3 S_1 + 5 S_1- 15[/tex] = 0Or, [tex]S_1 (S_1 - 3) + 5 (S_1 - 3)[/tex] = 0Or, [tex](S_1 - 3) ( S_1 + 5 )[/tex] = 0∴ [tex]S_1[/tex] = 3 , - 5 So, the running speed = 3 mile per hourAnd the biking speed = 15 mph + 3 mph = 18 mile per hourHence The running speed of Stu is 3 mile per hour  .  Answer