Question 1173083
speed*time=distance
x *y=5, where x is speed in km/h and y is time in hours
on way back it ix (x+1)*(2.5-y)=5

since the two equations are equal to 5, they are equal to each other
so xy=2.5x-xy+2.5-y or 5=2.5x-5+2.5-y, or 7.5=2.5x-y
x=(5/y)
so 7.5=2.5*(5/y)-y
7.5=(12.5/y)-y
y^2+7.5y-12.5=0
or 2y^2+15y-25=0
y=(1/4)(-15+/- sqrt(225+200)) sqrt(425)=20.62
so y=5.62/4=1.405 hr.only positive root

x=3.559 km/h for 1.405 hr. This is the answer,
on way back it was 4.559 km/h for 1.096 hr.