SOLUTION: In a walkathon to raise money for a charity, Elisa walked a certin distance at 5mi/h and then jogged twice that distance at 8mi/h. Her total time walking and jogging was 2 h and 15

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Question 214179: In a walkathon to raise money for a charity, Elisa walked a certin distance at 5mi/h and then jogged twice that distance at 8mi/h. Her total time walking and jogging was 2 h and 15 min. How many miles long was the walkathon? ( hint: time equals distance over rate.)
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
I would write 2 equations, 1 for
jogging and 1 for walking
d%5Bj%5D+=+r%5Bj%5D%2At%5Bj%5D
d%5Bw%5D+=+r%5Bw%5D%2At%5Bw%5D
----------------------
given:
r%5Bj%5D+=+8 mi/hr
r%5Bw%5D+=+5 mi/hr
d%5Bj%5D+=+2d%5Bw%5D
t%5Bj%5D+%2B+t%5Bw%5D+=+2.25 hrs
------------------------
Now rewrite the equations
d%5Bj%5D+=+r%5Bj%5D%2At%5Bj%5D
2d%5Bw%5D+=+8%2A%282.25+-+t%5Bw%5D%29
2d%5Bw%5D+=+18+-+8t%5Bw%5D
d%5Bw%5D+%2B+4t%5Bw%5D+=+9
and
d%5Bw%5D+=+r%5Bw%5D%2At%5Bw%5D
d%5Bw%5D+=+5t%5Bw%5D
Substituting:
5t%5Bw%5D+%2B+4t%5Bw%5D+=+9
9t%5Bw%5D+=+9
t%5Bw%5D+=+1 hr
And, since
d%5Bw%5D+=+5t%5Bw%5D
d%5Bw%5D+=+5 mi
And, since
d%5Bj%5D+=+2d%5Bw%5D
d%5Bj%5D+=+2%2A5
d%5Bj%5D+=+10 mi
The walkathon was 5+%2B+10+=+15 mi
check:
d%5Bj%5D+=+r%5Bj%5D%2At%5Bj%5D
10+=+8%2At%5Bj%5D
t%5Bj%5D+=+1.25 hr
and
d%5Bw%5D+=+r%5Bw%5D%2At%5Bw%5D
5+=+5%2At%5Bw%5D
t%5Bw%5D+=+1 hr
t%5Bj%5D+%2B+t%5Bw%5D+=+2.25
OK