Question

A person on a road trip drives a car at different constant speeds over several legs of the trip. She drives for 35.0 min at 50.0 km/h, 19.0 min at 55.0 km/h, and 50.0 min at 40.0 km/h and spends 25.0 min eating lunch and buying gas.(a)What is the total distance traveled over the entire trip (in km)? ______km(b)What is the average speed for the entire trip (in km/h)?_______ km/h

Answer 1

Part a)

Remember that one hour has 60 minutes. Then, a minute is 1/60 of an hour.

Convert minutes to hours and find the distance traveled over the entire trip using the formula:

`d=vt`

Then, the distances covered on each leg of the trip are:

`\begin{gathered} d_1=\left(50.0(km)/(h)\right)\left(35.0min*(1h)/(60min)\right)=29.16...km \\ \\ d_2=\left(55.0(km)/(h)\right)\left(19.0min*(1h)/(60min)\right)=17.42...km \\ \\ d_3=\left(40.0(km)/(h)\right)\left(50.0min*(1h)/(60min)\right)=33.33...km \\ \\ d_4=\left(0(km)/(h)\right)\left(25.0min*(1h)/(60min)\right)=0km \end{gathered}`

Then, the total distance traveled is:

`\begin{gathered} d=d_1+d_2+d_3+d_4 \\ \\ =29.16...km+17.42...km+33.33...km+0km \\ \\ =79.91...km \end{gathered}`

Part b)

The average speed of the entire trip is the total distance traveled over the time that it takes to travel that distance.

The total time that it took for the trip was:

`\begin{gathered} t=t_1+t_2+t_3+t_4 \\ \\ =35.0min+19.0min+50.0min+25.0min \\ \\ =129.0min \end{gathered}`

Then, the average speed for the entire trip, was:

`v=(d)/(t)=(79.91km)/(129.0min*(1h)/(60min))=37.167...(km)/(h)`

Therefore, the answers are:

A) 79.9km

B) 37.2 km/h