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# Driving at a constant speed, Sharon usually takes 180 minutes to drive from her house

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Driving at a constant speed, Sharon usually takes 180 minutes to drive from her house to her mother's house. One day Sharon begins the drive at her usual speed, but after driving 1/3​ of the way, she hits a bad snowstorm and reduces her speed by 20 miles per hour. This time the trip takes her a total of 276 minutes. How many miles is the drive from Sharon's house to her mother's house?

May 10, 2022

#1
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Let her average speed for the first 1/3 of her drive==S

Let the distance between her house and her mother's house==D

D / S ==180 / 60

1/3D / S  +  2/3D / (S - 20) ==276 / 60

S==45 mph - Her average speed.

D ==135 miles - distance between her house and her mother's house.

May 10, 2022
#2
+117821
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Let the entire distance be 3x

Normally that takes 180 minutes

speed would be  (3x)/180  =  x/60   miles per minute

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Storm day

It would take 60 minutes to go the first distance of x

then

276-60 = 216 minutes to go the next leg of 2x

speed is   $$\frac{x}{60}-\frac{20}{60}=\frac{x-20}{60}\;miles\; per \;minute$$

speed = distance /time

$$\frac{x-20}{60}=\frac{2x}{216}\\ \frac{x-20}{60}=\frac{2x}{27*8}\\ \frac{x-20}{10}=\frac{x}{18}\\ 18x-360=10x\\ 8x=360\\ x=45 miles\\ Total \;\;distance = 3*45 = 135miles.$$

May 10, 2022