Question 249444
The elapsed time is 4 hr of which 2.5 hr was driving time.
The distance formula is d = rt, where d=distance, r=rate, t=time
We assume the distance to her sister's is the same as it is home (or she drives the same path both ways without any detours).
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We can define the equation for driving to her sister's house:
d = 45(t)
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Then the equation for driving home from her sister's house is:
d = 55(2.5-t)
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In this way, we have defined the two unknown times in terms of a single unknown variable 't' and '2.5-t'.
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Since d = d, we can say:
45t = 55(2.5-t)
45t = 137.5 - 55t
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Adding 55t to both sides
100t = 137.5
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Dividing both sides by 100
t = 1.375
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So the time spend driving to her sister's house at 45 mph = 1.375 hr
The time spend driving home at 55 mph = 2.5 - 1.375 =  1.125 hr
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How far does she travel at 45 mph?
d = 45 mph * 1.375 hr = 61.875 miles.
How far does she travel at 55 mph?
d = 55 mph * 1.125 hr = 61.875 miles.
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So we've checked our work and are confident the distance is 61.875 = 61 7/8 miles.
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We could be asked what her average speed was, too.
Was it simply (45+55)/2?
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Well, we see that 2d = 2*61.875 = 123.75 miles
And it took 2.5 hr, so
t = d/r = 123.75/2.5 = 49.5.
So her average speed was 49.5.
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Done.