Mathematics: Acar moves uphill at 40 km/h and then back downhill at 60 km/h.what is the average speed for the round trip?

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Acar moves uphill at 40 km/h and then back downhill

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batmanmarie2004

02.01.2022

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
$t_{1} = \frac{(d \, km)}{(40 \, \frac{km}{h})} = \frac{d}{40}\, hours$
Similarly, the time to travel downhill is
$t_{2} = \frac{d}{60} \, hours$

The total travel time is
$t=t_{1}+t_{2} = \frac{d}{40} + \frac{d}{60} = \frac{60d+40d}{2400} = \frac{d}{24}\, hours$

The total distance traveled = 2d km

The average speed is
$v= \frac{(2d \, km)}{( \frac{d}{24} \, h)}=48\, \frac{km}{h}$

The average speed is 48 km/h

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Acar moves uphill at 40 km/h and then back downhill at 60 km/h.what is the average speed for the round trip?

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