SOLUTION: A ferry leaves a harbor and travels to a resort island at an average speed of 18 mph. On the return trip, because of fog, the ferry travels at an average speed of 10 mph. The total

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Question 1187907: A ferry leaves a harbor and travels to a resort island at an average speed of 18 mph. On the return trip, because of fog, the ferry travels at an average speed of 10 mph. The total time for the trip is 7 h. How far is the island from the harbor?
Found 2 solutions by Alan3354, greenestamps:
Answer by Alan3354(69443) (Show Source):
You can put this solution on YOUR website!
A ferry leaves a harbor and travels to a resort island at an average speed of 18 mph. On the return trip, because of fog, the ferry travels at an average speed of 10 mph. The total time for the trip is 7 h. How far is the island from the harbor?
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Avg speed of any round trip is
RT distance = Avg speed*7 hours

Answer by greenestamps(13200) (Show Source):
You can put this solution on YOUR website!

(1) A standard algebraic setup for solving the problem....

d = distance (miles)

d/18 = time (hours) for outbound trip at 18mph
d/10 = time (hours) for return trip at 10mph

The total time is 7 hours:

Solve using basic algebra....

Multiply by the least common denominator, 90:

ANSWER: 45 miles

(2) An informal solution using logical reasoning and simple mental arithmetic....

The distances out and back are the same, so the ratio of the times spent on the two legs of the trip is the same as the ratio of the two speeds.

The ratio of speeds for the first and second legs is 18:10 = 9:5.

So the ratio of times spent on the first and second legs is 5:9.

The total time was 7 hours, so

time spent on outbound leg: (5/14)(7) hours = 2.5 hours
time spent on return leg: (9/14)(7) hours = 4.5 hours

Length of each leg:
(2.5 hours)*(18mph) = 45 miles
or
(4.5 hours)*(10mph) = 45 miles

ANSWER: 45 miles