SOLUTION: Jamie recently drove to visit her parents who live 560 miles away. On her way there her average speed was 24 miles per hour faster than on her way home (she ran into some bad weath

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Question 1087930: Jamie recently drove to visit her parents who live 560 miles away. On her way there her average speed was 24 miles per hour faster than on her way home (she ran into some bad weather). If Jamie spent a total of 16 hours driving, find the two rates.
Found 2 solutions by josgarithmetic, ikleyn:
Answer by josgarithmetic(39618) About Me  (Show Source):
You can put this solution on YOUR website!
Speed going to her parents , r+24
Speed coming back home, r


                     RATE          TIME          DISTANCE
GOING TO             r+24          560/(r+24)      560
RETURN HOME          r             560/r           560
Total                               16

560%2F%28r%2B24%29%2B560%2Fr=16
-

35%2F%28r%2B24%29%2B35%2Fr=1
35r%2B35%28r%2B24%29=r%5E2%2B24r
35r%2B35r%2B35%2A24=r%5E2%2B24r
r%5E2%2B24r-70r-35%2A24=0
r%5E2-46r-35%2A24=0
-
discriminant is 74%5E2

r=%2846%2B-+74%29%2F2
choose the positive value of r.
r=%2846%2B74%29%2F2
highlight%28r=60%29, trip home, speed
highlight%2884%29, trip going to parents

Answer by ikleyn(52793) About Me  (Show Source):
You can put this solution on YOUR website!
.
Let u be the Jamie slower rate, in miles per hour (mph).

Then her faster rate is (u+24) mph.


Time at slower rate is 560%2Fu hours.

Time at faster rate is 560%2F%28u%2B24%29 hours.


The time for the two-way journey is the sum of these values, which gives you an equation

560%2Fu  + 560%2F%28u%2B24%29 = 16    hours.


The setup is done.

To solve the equation, multiply both sides by u*(u+24). You will get

560*(u+24) + 560u = 16u*(u+24).


Simplify and solve this quadratic equation to get the answer u = 60 mph.


Answer.  The slower speed was 60 mph.  The faster speed was 60+24 = 84.

Solved.