Question

Julie drives 100 mi to Grandmother's house. On the way to Grandmother's, Julie drives half the distance at 44.0mph and half the distance at 72.0mph . On her return trip, she drives half the time at 44.0mph and half the time at 72.0mph . What is her average speed on the return trip?

Answer 1

Let the time taken for the total return trip be t hours.
Distance = speed * time
Distance travelled at 44 mph = 44 * (t/2) ..........(1)
Distance travelled at 72 mph = 72 * (t/2) ..........(2)

The total distance travelled is 100 miles. Therefore
\[100=(44\times\frac{t}{2})+(72\times\frac{t}{2})=22t+36t\ .......(3)\]
From equation (3) we find that
58t = 100
Therefore the time for the return trip is
\[t=\frac{100}{58}\ hours\ .........(4)\]
The average speed for the return trip is given by
\[Average\ speed=\frac{distance}{time}=\frac{100}{t}=\frac{100}{\frac{100}{58}}=\frac{100\times58}{100}\ mph\]

Answer 2

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