Arturo O. answered • 10/12/16
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v = speed of boat in still water = ?
w = speed of water = 1.5 km/hr
t1 = time to travel downstream = 5 hrs
t2 = time to travel upstream = 5.5 hrs
d = one-way distance, which is the same upstream and downstream
Downstream:
d = (v + w)t1
Upstream:
d = (v - w)t2
(v + w)t1 = (v - w)t2
(v + 1.5)(5) = (v - 1.5)(5.5)
5v + 7.5 = 5.5v - 8.25
0.5v = 15.75
v = 31.5 km/hr
The correct answer is (C).
Arturo O.
Along both the downstream and upstream trips you apply the relation
distance = speed x time
When going downstream, you get help from the speed of the water, so the net downstream speed of the boat is the sum of its speed in still water and the speed of the water: v + w
When going upstream, the speed of the water opposes the boat, so the net upstream speed of the boat is its speed in still water minus the speed of the water: v - w
The times of the downstream (t1) and upstream (t2) trips are given.
So just multiply the net downstream speed by the downstream travel time to get downstream distance:
d = (v + w)t1
Multiply the net upstream speed by the upstream travel time to get upstream distance:
d = (v - w)t2
The downstream and upstream distances are the same, so set them equal to each other:
(v + w)t1 = (v - w)t2
You are given the water speed w, and the times t1 and t2. Then just solve for v from the equation above.
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