# Question #4aa5a

##### 2 Answers

48 km/hr

#### Explanation:

Pick some distance the motorcyclist might have traveled (it doesn't matter what distance but for ease of calculation I chose 120 km).

Time spent traveling 120 km at 40 km/hr

Time spent traveling 120 km at 60 km/hr

Total time spent traveling

Average speed

The answer is **(b)**

#### Explanation:

I want to provide an alternative approach to figuring out the average sspeed of the motorcyclist.

So, you know that the motorcyclist travels *the same distance*, let's say

Let's assume that it takes him

This means that you can write

#d = 40 * t_1" "# and#" "d = 60 * t_2#

This is equivalent to

#40 * t_1 = 60 * t_2 implies t_1 = 3/2 * t_2#

The average speed of the motorcyclist can be thought of as the **total distance** he covered divided by the **total time** needed.

Since he goes from

#d_"total" = 2 * d#

The total time will be

#t_"total" = t_1 + t_2#

#t_"total" = 3/2 * t_2 + t_2 = 5/2 * t_2#

The average speed will thus be

#bar(v) = (2d)/(5/2 * t_2) = 4/5 * d/t_2#

But

#bar(v) = 4/5 * 60 = color(green)("48 km/h")#