Answer :
Answer:
Rate of Walking = 4 miles/hour
Rate of jogging = 8 miles/hour
Step-by-step explanation:
Let speed of walk be =[tex]x[/tex] miles/hour
Distance covered by walking = 8 miles
Time 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/hour
Distance covered by Jogging = 8 miles
Time 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 hours
so,
[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/hour
Rate of jogging = [tex]2x[/tex] = [tex]2\times 4 [/tex]= 8 miles/hour