Respuesta :
Answer:
Step-by-step explanation:
Given as :
The distance cover while running = [tex]D_1[/tex] = 5 miles
Let The speed for running = [tex]S_1[/tex]
The distance cover with bike = [tex]D_2[/tex] = 80 miles
The speed for biking = [tex]S_2[/tex] = 15 mph + [tex]S_1[/tex]
Total Time taken = 5 hours
Now 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] = 0
or, [tex]5 S_1^{2} -10 S_1 - 75[/tex] = 0
or, [tex] S_1^{2} -2 S_1 - 15[/tex] = 0
Or, [tex]S_1^{2} -3 S_1 + 5 S_1- 15[/tex] = 0
Or, [tex]S_1 (S_1 - 3) + 5 (S_1 - 3)[/tex] = 0
Or, [tex](S_1 - 3) ( S_1 + 5 )[/tex] = 0
∴ [tex]S_1[/tex] = 3 , - 5
So, the running speed = 3 mile per hour
And the biking speed = 15 mph + 3 mph = 18 mile per hour
Hence The running speed of Stu is 3 mile per hour . Answer
