Problema Solution
A motorboat can maintain a constant speed of 32 miles per hour relative to the water. The boat makes a trip upstream to a certain point in 10 minutes; the return trip takes 6 minutes. What is the speed of the current?
Answer provided by our tutors
Let
c = the speed of the current
v = 32 mph the speed of the motorboat
t1 = 10 min = 10/60 = 1/6 h the time of the trip upstream
t2 = 6 min = 6/60 = 1/10 hr the time of the return trip (downstream)
Traveling upstream the speed of the motorboat is: v - c
Traveling downstream the speed of the motorboat is: v + c
Since speed = distance/time follows distance = speed*time and the boat traveled the same distance in each direction:
(v - c)*t1 = (v + c)*t2
(32 - c)*(1/6) = (32 + c)(1/10)
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click here to see the speed of the current calculation
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c = 8 mph
The speed of the current is 8 mph.