Answer:
The road will save Mr. Schmidt 3 5/24miles ( [tex]3\frac{5}{24}miles[/tex] )
Step-by-step explanation:
If Mr. Schmidt drives to work on the two straight roads, the distance he will cover will be the sum of the length of each road.
From the question,
One road is 6 1/3 miles long and the other road is 4 3/4 miles long
Hence he will cover a distance of
[tex]6\frac{1}{3}miles + 4\frac{3}{4} miles[/tex]
Then,
[tex]\frac{19}{3} + \frac{19}{4}[/tex]
= [tex]\frac{76+57}{12}[/tex]
= [tex]\frac{133}{12}[/tex]
= [tex]11\frac{1}{12}miles[/tex]
Hence, if He drives to work on the two straight roads, he will cover 11 1/2 miles.
From the question, if a direct road were built between Mr.Schmidt and Haworthorne, it would be 7 7/8 miles long.
Now, to determine how many miles this road would save Mr. Schmidt each trip,
We will find the difference pf the distance he will cover driving on the two straight roads and the distance of this road, that is
11 1/2 miles - 7 7/8 miles
[tex]11\frac{1}{12}miles - 7\frac{7}{8}miles[/tex]
Then,
=[tex]\frac{133}{12}- \frac{63}{8}[/tex]
= [tex]\frac{266-189}{24}[/tex]
= [tex]\frac{77}{24}[/tex]
[tex]3\frac{5}{24}miles[/tex]
Hence, the road will save Mr. Schmidt 3 5/24miles ( [tex]3\frac{5}{24}miles[/tex] )
