Question

Sierra drove five miles to stevens house at thirty six mph. she then drove seventeen miles to amanda's house. for the entire trip, sierra averaged a speed of 42 18/31 mph. what was her average speed driving from stevens to amanda's house?

Answer 1

The average speed of Sierra for driving from Steven's house to Amanda's house is 45mph.

We are given that the distance from Sierra's house to Steven's house is 5 miles and Sierra drove at the speed of 36mph.

Also the distance from Steven's house to Amanda's house is 17 miles.

The average speed of Sierra for the whole journey is $42\frac{18}{31} mph$.

We know that,

$Speed =\frac{Distance}{Time} \\\\Hence,\\\\Time=\frac{Distance}{Speed} \\\\Time =\frac{5}{36}hours$

Hence, time taken by Sierra to reach Steven's house is $\frac{5}{36} hours$.

Now,

Overall distance travelled By Sierra = 5 + 17 = 22 miles

Average speed for the journey = $42\frac{18}{31} mph=\frac{1320}{31}mph$

Hence,

Time taken for the whole journey = $\frac{22}{\frac{1320}{31} } =\frac{31}{60} hours$

Hence,

Total time taken = $\frac{5}{36}$+ Time taken to drive to Amanda's house from       Steven's house

Hence,

$\frac{31}{60}=\frac{5}{36}$+ Time taken to drive to Amanda's house from Steven's house

Time taken to drive to Amanda's house from Steven's house=

$\frac{31}{60}-\frac{5}{36}=\frac{93-25}{180}=\frac{68}{180}=\frac{17}{45} hours$

Hence,

Speed when Sierra is driving from Steven's house to Amanda's house =

$\frac{17}{\frac{17}{45} }=\frac{17}{1}*\frac{45}{17}= 45mph$

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