Problema Solution
A boat traveled downstream a distance of
27 mi and then came right back. If the speed of the current was
12 mph and the total trip took 3 hours, find the average speed of the boat relative to the water.
Answer provided by our tutors
Let
d = 27 mi the distance traveled in one direction
c = 12 mph the speed of the current
t = 3 hr the total time of the travel
v = the average speed of the boat relative to the water
The speed of the boat traveling with the current is: v + c
The speed of the boat traveling against the current is: v - c
Since speed = distance/time follows time = distance/speed:
d/(v + c) + d/(v - c) = t
27/(v + 12) + 27/(v - 12) = 3
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click here to see the equation solved for v
........
v = 24 mph
We need to ignore the negative solution -6 since the speed is a positive number.
The average speed of the boat relative to the water is 24 mph.