Question 1074799
speed there was x+21 mph and time was 864/x+21hours. S*t=distance
speed back was (x) mph and time was 864/x hours.
The two times add to 24
so 864/x+864/(x+21)=24
multiply both sides by x(x+21)
864(x+21)+864(x)=24(x(x+21))
864x+18144+864x=24x^2+504x
0=24x^2-1224x-18144
divide by 24
x^2-51x-756=0
(x-63)(x+12)=0
x=63 mph, only positive root speed back, which took 864/63 or 13.71 hours.
x+21=84 mph, which took 10.29 hours there.
Total is 24 hours.