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

#### Solution:

### Let D represent the distance up the hill, which is also equal to the distance down the hill. We know that going up the hill, the car had a constant speed of 40km/h and going down the hill, it had a constant speed of 60km/h. The speed, v, is equal to \frac{D}{t}. Therefore, the average speed can be written as, the total distance going up and down divided by the total time taken:

### v=\frac{D_{up}+D_{down}}{t_{up}+t_{down}}

##### (note that the distance going up the hill is the same as going down the hill)

### =\frac{2D}{\frac{D}{v_{up}}+ \frac{D}{v_{down}}}

### We can simplify this by canceling the D’s out, and if we plug in v_{up}=40 km/h and v_{down}=60 km/h , this yields an average speed of 48 km/h.

###### This is question can be found in Fundamentals of Physics, 10th edition, chapter 2, question 4.