Half the Distance and Half the Time Problem| University Physics

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

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

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

and for the next 50 miles, she drove for

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

Therefore, her average speed was

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

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