SOLUTION: 1) At noon Joyce drove to the lake at 30 miles per hour, but she made the long walk back home at 4 miles per hour. How long did she walk if she was gone for 17 hours? How far did s

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Question 141558This question is from textbook Algebra 1
: 1) At noon Joyce drove to the lake at 30 miles per hour, but she made the long walk back home at 4 miles per hour. How long did she walk if she was gone for 17 hours? How far did she walk? Begin by drawing a diagram of distances traveled and writing the distances equations.
2) Nine sixteenths of the girls belived that saltations was salubrious. If the other 700 girls were undecided, how many girls had made their minds concerning this topic? This question is from textbook Algebra 1

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1) At noon Joyce drove to the lake at 30 miles per hour, but she made the long walk back home at 4 miles per hour. How long did she walk if she was gone for 17 hours? How far did she walk? Begin by drawing a diagram of distances traveled and writing the distances equations.
:
Let d = distance to the lake
:
*>------------------->---d-@-30-mph------------------*lake
*-----------d-@-4-mph-------<-----------------------<*lake
:
Write a time equation: Time = dist%2Fspeed; find d
:
Drive time + walk time = 17 hrs
d%2F30 + d%2F4 = 17
Multiply equation by 30 to get rid of the denominators:
2d + 15d = 17(60)
17d = 17(60)
d = 60 mi
:
:
Check solution by finding the times
Drive; 60/30 = 2 hrs
Walk:: 60/4 = 15 hrs
---------------------
total hours = 17 hrs
;
:
2) Nine sixteenths of the girls belived that saltations was salubrious. If the other 700 girls were undecided, how many girls had made their minds concerning this topic?
:
Let x = the total number of girls
The other 700 would be 7/16
7%2F16x = 700
7x = 700 * 16
7x = 11200
x = 11200%2F7
x = 1600 total girls
;
9%2F16*1600 = 900 made up their minds