SOLUTION: Susie drove 100 miles to visit a friend. If she had driven 8 miles per hour faster than she did, she would have arrived in 5/6 of the time it actually took. How many minutes did th

Algebra ->  Customizable Word Problem Solvers  -> Travel -> SOLUTION: Susie drove 100 miles to visit a friend. If she had driven 8 miles per hour faster than she did, she would have arrived in 5/6 of the time it actually took. How many minutes did th      Log On

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Question 890866: Susie drove 100 miles to visit a friend. If she had driven 8 miles per hour faster than she did, she would have arrived in 5/6 of the time it actually took. How many minutes did the trip take?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +s+ = the speed in mi/hr that would
get her there non time
Let +t+ = time in hrs spent driving to
get her there on time
---------------------------
(1) +100+=+s%2At+
(2) +100+=+%28+s+%2B+8+%29%2A%28%285%2F6%29%2At+%29+
----------------------------
(2) +600+=+%28+s+%2B+8+%29%2A5t+
and
(1) +t+=+100%2Fs+
Substitute (1) into (2)
(2) +600+=+%28+s+%2B+8+%29%2A5%2A%28+100%2Fs+%29+
(2) +600s+=+500%2A%28+s+%2B+8+%29+
(2) +600s+=+500s+%2B+4000+
(2) +100s+=+4000+
(2) +s+=+40+
-------------------
(1) +t+=+100%2Fs+
(1) +t+=+100%2F40+
(1) +t+=+5%2F2+ hrs
The trip actually took +60+%2A+%285%2F2%29+=+150+ minutes
check:
(2)
(2) +100+=+25%2A4+
(2) +100+=+100+
OK