Question

Julie drives 100 mi to Grandmother's house. On the way to Grandmother's, Julie drives half the distance at 34.0 mph and half the distance at 66.0 mph. On her return trip, she drives half the time at 34.0 mph and half the time at 66.0 mph. what is julies average speed on the way to grandmothers house?

Answer 1

The concepts necessary to solve this problem are those given by the kinematic equations of motion. We will apply the speed as a unit of distance traveled in a given time.

The total distance of 50 miles is traveled with a speed of 34mph in the time $T_1$ and the distance of another 50 miles is traveled with a speed 66mph in the time $T_2$.

Determine the value of $T_1$ as follows.

$t = \frac{d}{v}$ $\rightarrow$ Where t=time, d=distance, v= Velocity

$t = \frac{50miles}{34mph}$

$t = 1.471h$

Determine the value of $T_2$ as

$T_2 = \frac{50miles}{66mph}$

$T_2 = 0.7576h$

Therefore the total time taken is

$T_{Total} = T_1+T_2$

$T_{Total} = 1.471h+0.7576h$

$T_{Total} = 2.2286h$

The above result is the total time taken to reach the grandmother's house

Now the average velocity is

$v_{Avg} = \frac{100 miles}{2.2286h}$

$v_{Avg} = 44.87mph$

Therefore the average speed on the way to grandmother's house is 44.87mph