Question

A person travels by car from one city to another with different constant speeds between pairs of cities. She drives for 15.0 min at 85.0 km/h, 19.0 min at 80.0 km/h, and 30.0 min at 45.0 km/h and spends 45.0 min eating lunch and buying gas.(a) Determine the average speed for the trip._____ km/h(b) Determine the distance between the initial and final cities along the route._____ km

Answer 1

We will have the following:

a) We determine the average speed for the trip as follows:

`\begin{gathered} s_a=(((85km/h)(0.25h)+(80km/h)(19/60h)+(45km/h)(0.5h))/(109/60h))/(3) \\ \\ \Rightarrow s_a=(4145)/(327)km/h\Rightarrow s_a\approx12.68km/h \end{gathered}`

So, the average speed of the whole travel is approximatey 12.68 km/h.

b) We determine the distance between the intitial and final cities as follows:

`\begin{gathered} d=(85km/h)(0.25h)+(80km/h)(19/60h)+(45km/h)(0.5h)\Rightarrow d=(829)/(12)km \\ \\ \Rightarrow d\approx69.08km \end{gathered}`

So, the distance is approximatey 69.08 km between the cities.