SOLUTION: A ferry leaves a harbor and travels to a resort island at an average speed of 20 mph. On the return trip, the ferry travels at an average speed of 12 mph because of fog. The total

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Question 396744: A ferry leaves a harbor and travels to a resort island at an average speed of 20 mph. On the return trip, the ferry travels at an average speed of 12 mph because of fog. The total time for the trip is 5 h. How far is the island from the harbor?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Going to island:
d+=+r%2At%5B1%5D
d+=+20t%5B1%5D
Returning from island
d+=+12%2At%5B2%5D
I also can say
t%5B1%5D+%2B+t%5B2%5D+=+5 hrs
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The distance is the same going and coming, so
20t%5B1%5D=+12%2At%5B2%5D
and
t%5B2%5D+=+5+-+t%5B1%5D
substituting:
20t%5B1%5D+=+12%2A%285+-+t%5B1%5D%29
20t%5B1%5D+=+60+-+12t%5B1%5D
32t%5B1%5D+=+60
t%5B1%5D+=+15%2F8 hrs
and
t%5B2%5D+=+5+-+15%2F8
t%5B2%5D+=25%2F8 hrs
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d+=+20%2At%5B1%5D
d+=+20%2A%2815%2F8%29
d+=+37.5
the distance to the island is 37.5 mi
check:
d+=+12%2At%5B2%5D
d+=+12%2A%2825%2F8%29
d+=+37.5 mi
OK