Question

Suzie and Scott drive together for American freight. One day Suzie averaged 54 mph and Scott average 58mph, but Scott drove for 3 more hours than Suzie. If together they drove 734 miles, then for how many hours did Scott drive?

Answer 1

`t_2=8h`

Explanation:

`v_1=54mph`
`v_2=58mph`
`Deltat=3h`
`t_2=t_1+Deltat => t_1=t2-Deltat`
`s=s_1+s_2=734m`
`t_2=?`

`s_1=v_1*t_1`
`s_2=v_2*t_2`
`s=v_1*t_1+v_2*t_2`
`s=v_1*(t_2-Deltat)+v_2*t_2`
`s=v_1*t_2-v_1*Deltat+v_2*t_2`
`s=t_2*(v_1+v_2)-v_1*Deltat`
`t_2*(v_1+v_2)=s+v_1*Deltat`

`t_2=(s+v_1*Deltat)/(v_1+v_2)`

`t_2=(734m+54mph*3h)/(54mph+58mph)=(734m+162m)/(112mph)=(896m)/(112mph)`

`t_2=8h`