Question

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 1

Rate of Walking = 4 miles/hour

Rate of jogging = 8 miles/hour

Explanation:

Let speed of walk be =
`x` miles/hour

Distance covered by walking = 8 miles

Time taken to walk 8 miles =
`(Distance)/(speed)=(8)/(x)`

Speed of jog is twice walking speed and that =
`2x` miles/hour

Distance covered by Jogging = 8 miles

Time taken to jog 8 miles=
`(Distance)/(speed)=(8)/(2x)=(4)/(x)`

Total time taken to walk and jog=
`(8)/(x)+(4)/(x)`

Total time actually taken =3 hours

so,

`(8)/(x)+(4)/(x)=3`

Taking LCD and adding fractions.

`(12)/(x)=3`

Multiplying both sides by
`x`.

`x*(12)/(x)=3* x\\\\12=3x`

Dividing both sides by 3.

`(12)/(3)=(3x)/(3)\\\\4=x`

∴ Rate of Walking =
`x` = 4 miles/hour

Rate of jogging =
`2x` =
`2* 4`= 8 miles/hour