SOLUTION: I need help on this plz A girl starts to walk to her school, which is 20 miles away, at 6:50 and at a rate of 3 miles per hour. After a while, her dad picks her up and drives her t

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Question 1028613: I need help on this plz A girl starts to walk to her school, which is 20 miles away, at 6:50 and at a rate of 3 miles per hour. After a while, her dad picks her up and drives her through the remainder of the way at 30 miles per hour. If they arrived at school at 9:00, how far did she walk?
Found 2 solutions by ankor@dixie-net.com, KMST:
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
A girl starts to walk to her school, which is 20 miles away, at 6:50 and at a rate of 3 miles per hour.
After a while, her dad picks her up and drives her through the remainder of the way at 30 miles per hour.
If they arrived at school at 9:00, how far did she walk?
:
Find the total time it took her to get to school: 9:00 - 6:50 = 2 hrs 10 min
Change this to hrs; 2 1%2F6hrs which is 13%2F6 hr
:
let w = distance walked
the total dist is 20 mi, therefore
(20-w) = distance driven
:
Write a time equation, time = dist/speed
Walk time + drive time = 13%2F6 hrs
w%2F3 + %2820-w%29%2F30 = 13%2F6
get rid of the fractions, multiply equations by 30, then cancel
10w + (20-w) = 5(13)
10w - w = 65 - 20
9w = 45
w = 45/9
w = 5 miles walked
;
:
Check this by finding the actual time walking (5mi) and riding (15mi)
5/3 = 1.67 hrs
15/30 = .5 hrs
---------------
total time 2.17 hrs which is 2 hrs 10 min

Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
DISCLAIMER: No guarantees that this is the way your teacher thinks the problem should be solved. (The result is correct, though).

ONE WAY:
x= distance the girl walked, in miles
20-x= distance the girl rode in her dad's car, in miles
d%2F3= time the girl spent walking towards school, in hours
%2830-d%29%2F30= time the girl spent riding in her dad's car towards school, in hours
%222+hours+10+minutes%22=2%261%2F6hours=13%2F6hours= total time walking and riding to school
d%2F3%2B%2830-d%29%2F30=13%2F6 is our equation.
Multiplying times 30 ,
10d%2B30-d=65
10d-d=65-30
9d=45
d=45%2F9
highlight%28d=5%29
So the girl walked highlight%285miles%29 before her dad picked her up.

USING SYSTEMS OF EQUATIONS:
x= time walking to school, in hours
y= time riding to school, in hours
x%2By=130%2F60=13%2F6= total time walking and riding to school
3x= miles walked to school
30y= miles traveled by car going to school
3x%2B30y=20
system%28x%2By=13%2F6%2C3x%2B30y=20%29-->system%2830x%2B30y=65%2C3x%2B30y=20%29-->27x=45%29-->x=5%2F3-->3x=highlight%285%29
So the girl walked highlight%285miles%29 before her dad picked her up.