SOLUTION: A bus traveled on a straight road for 2 hours at an average speed that was 20 mph faster than its average speed on a winding road.The time spent on the winding road was 3 hours. Fi

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Question 192839: A bus traveled on a straight road for 2 hours at an average speed that was 20 mph faster than its average speed on a winding road.The time spent on the winding road was 3 hours. Find the average speed on the winding if the total trip was 210 miles.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let s%5Bw%5D = the average speed on the winding road
given:
d%5Bs%5D+=+s%5Bs%5D%2At%5Bs%5D
d%5Bw%5D+=+s%5Bw%5D%2At%5Bw%5D
d%5Bs%5D+%2B+d%5Bw%5D+=+210
t%5Bs%5D+=+2 hr
t%5Bw%5D+=+3 hr
s%5Bs%5D+=+s%5Bw%5D+%2B+20
----------------
d%5Bs%5D+=+s%5Bs%5D%2A2
210+-+d%5Bs%5D+=%28+s%5Bs%5D+-+20%29%2A3
210+-+2s%5Bs%5D+=+3s%5Bs%5D+-+60
5s%5Bs%5D+=+270
s%5Bs%5D+=+54 mi/hr
and, since
s%5Bs%5D+=+s%5Bw%5D+%2B+20
54+=+s%5Bw%5D+%2B+20
s%5Bw%5D+=+34 mi/hr
The average speed on the winding road was 34 mi/hr
check answer:
d%5Bs%5D+=+s%5Bs%5D%2At%5Bs%5D
d%5Bs%5D+=+54%2A2
d%5Bs%5D+=+108 mi
and
d%5Bw%5D+=+s%5Bw%5D%2At%5Bw%5D
d%5Bw%5D+=+34%2A3
d%5Bw%5D+=+102 mi
and
108+%2B+102+=+210 mi
OK