Define d = distance (km) traveled in either direction t₁ = time (hours) to travel uphill t₂ = time(hours) to tavel downhill
The time to travel uphill is [tex]t_{1} = \frac{(d \, km)}{(40 \, \frac{km}{h})} = \frac{d}{40}\, hours [/tex] Similarly, the time to travel downhill is [tex]t_{2} = \frac{d}{60} \, hours[/tex]
The total travel time is [tex]t=t_{1}+t_{2} = \frac{d}{40} + \frac{d}{60} = \frac{60d+40d}{2400} = \frac{d}{24}\, hours [/tex]
The total distance traveled = 2d km
The average speed is [tex]v= \frac{(2d \, km)}{( \frac{d}{24} \, h)}=48\, \frac{km}{h} [/tex]
