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?
February 20th, 2023
##t_2=8h##
##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##