A motorist travels 160km at 80km/h and 160km at 100km/h. What is the average speed of the motorist for this trip?

The average speed of the motorist = `"Total Distance"/"Total time Elapsed"`

Calculation for the first leg

= `\frac{"160 km"}{80 \frac{"km"}{"h"}}`

= 2 h

and for the second leg,

= `\frac{"100 km"}{80 \frac{"km"}{"h"}}`

= 1.6 h (1 hour 60 minutes)

Giving a total travel time of 3.6 hours (2 hours + 1.6 hours).

The average speed over the total duration is then,

`\overline{v}` = `\frac{"160 km + 160 km"}{"3.6 h"}`

= 88.9 `"km"/"h"`