algebra word problem help!?
a boat traveled downstream a distance of 55 mi and then came right back. if the speed of the current was 30mph and the total trip took 3 hours and 40 minutes, find the average speed of the boat relative to the water.
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Let
V = speed of the boat, relative to the water
T₁ = time needed to travel downstream
T₂ = time needed to travel upstream
When traveling downstream:
(V + 30)×T₁ = 55 . . . . . . . . . . . . . . . . . . . . . equation 1
When traveling upstream:
(V - 30)×T₂ = 55 . . . . . . . . . . . . . . . . . . . . . equation 2
You also know that
T₁ + T₂ = 3h 40 min
T₁ + T₂ = 11/3 h . . . . . . . . . . . . . . . . . . . . . equation 3
Solving this 3×3 system, you will find that:
T₁ = 4.8 h
T₂ = -1.1 h
V = -18.5 mph
or
T₁ = 0.70 h
T₂ = 2.97 h
V = 48.5 mph
Obviously, the first solution is impossible (negative time for T₂), which means that:
V = 48.5 mph < - - - - - - - - answer