As part of an exercise regimen, you walk 8 miles on an indoor track. Then you jog at twice your walking speed for another 8 miles. If the total spent walking and jogging is 3 hours, find the walking and jogging rates

Answer:Rate of Walking = 4 miles/hourRate of jogging = 8 miles/hourStep-by-step explanation:Let speed of walk be =[tex]x[/tex] miles/hourDistance covered by walking = 8 milesTime taken to walk 8 miles = [tex]\frac{Distance}{speed}=\frac{8}{x}[/tex]Speed of jog is twice walking speed and that = [tex]2x[/tex] miles/hourDistance covered by Jogging = 8 milesTime taken to jog 8 miles=  [tex]\frac{Distance}{speed}=\frac{8}{2x}=\frac{4}{x}[/tex]Total time taken to walk and jog= [tex]\frac{8}{x}+\frac{4}{x}[/tex]Total time actually taken =3 hoursso,[tex]\frac{8}{x}+\frac{4}{x}=3[/tex]Taking LCD and adding fractions.[tex]\frac{12}{x}=3[/tex]Multiplying both sides by [tex]x[/tex].[tex]x\times\frac{12}{x}=3\times x\\\\12=3x[/tex]Dividing both sides by 3.[tex]\frac{12}{3}=\frac{3x}{3}\\\\4=x[/tex]∴ Rate of Walking = [tex]x[/tex] = 4 miles/hourRate of jogging = [tex]2x[/tex] = [tex]2\times 4 [/tex]= 8 miles/hour