Half the Distance and Half the Time Problem| University Physics

Julie drives 100 mi to Grandmother’s house. On the way to Grandmother’s, Julie drives half the distance at 35.0 mph and half the distance at 65.0 mph. On her return trip, she drives half the time at 35.0 mph and half the time at 65.0 mph.

PART A. What is Julie’s average speed on the way to Grandmother’s house?

ANSWER: 45.5 mph

Julie drove 50 miles at a speed of 35 mph, and drove another 50 miles for 65 mph. So, for the first 50 miles, she drove for

\displaystyle time=\frac{distance}{speed}=\frac{50\:mi}{35\:mph}=\frac{10}{7}\:hours

and for the next 50 miles, she drove for

\displaystyle time=\frac{distance}{speed}=\frac{50\:mi}{65\:mph}=\frac{10}{13}\:hours

Therefore, her average speed was

\displaystyle average\:speed=\frac{total\:distance}{total\:time}

\displaystyle average\:speed=\frac{100\:miles}{\frac{10}{7}+\frac{10}{13}\:hours}=45.5\:mph

PART B. What is her average speed on the return trip?

ANSWER: 50.0 m/s

Since the time she used driving at 35 mph is the same amount of time she used driving at 65 mph, the average speed is just the average of the two speeds given.