A river 1.00 mile wide flows with a constant speed of 1.00 mi/h. A woman leaves from a point on the river bank. The woman rows a boat 1.00 mi directly upstream and returns to the starting point. Her speed in still water is 2.00 mi/h. The travel time for the woman is
A) 2.00 h. B) 1.15 h. C) 1.00 h. D) 1.33 h. E) 0.67 h.
since time = distance/speed,
1/(2-1) + 1/(2+1) = 1/1 + 1/3 = 4/3
Looks like (D) to me
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To find the travel time for the woman, we can use the concept of relative velocity.
Let's assume that the speed of the river's current is denoted by v and the speed of the woman in still water is denoted by w.
When the woman rows upstream, she is rowing against the current, so her effective speed will be reduced by the speed of the current. Her speed upstream is given by (w - v).
When the woman rows downstream, she is rowing with the current, so her effective speed will be increased by the speed of the current. Her speed downstream is given by (w + v).
Given that the width of the river is 1.00 mile and the speed of the river's current is 1.00 mi/h, we can substitute these values into the equations:
Speed upstream = (2.00 mi/h - 1.00 mi/h) = 1.00 mi/h
Speed downstream = (2.00 mi/h + 1.00 mi/h) = 3.00 mi/h
Now, we can calculate the time it takes for the woman to row upstream and downstream using the formula: Time = Distance / Speed.
Time upstream = 1.00 mile / 1.00 mi/h = 1.00 hour
Time downstream = 1.00 mile / 3.00 mi/h = 0.33 hours
Total travel time = Time upstream + Time downstream = 1.00 hour + 0.33 hours = 1.33 hours
Therefore, the correct answer is D) 1.33 hours.
To find the travel time of the woman, we need to consider the speed of the boat and the speed of the river.
Let's denote the speed of the boat in still water as "b" and the speed of the river as "r."
Given:
Speed of the boat in still water (b) = 2.00 mi/h
Speed of the river (r) = 1.00 mi/h
When the woman is traveling upstream (against the current), the effective speed of the boat is reduced by the speed of the river, since it's working against the current. Therefore, the effective speed is (b - r).
When the woman is traveling downstream (with the current), the effective speed of the boat is increased by the speed of the river, since it's assisting the boat. Therefore, the effective speed is (b + r).
Now, let's calculate the time taken for each leg of the journey:
1. Upstream leg:
Distance = 1.00 mile
Speed = (b - r) = (2.00 - 1.00) = 1.00 mi/h
Time = Distance / Speed = 1.00 mile / 1.00 mi/h = 1.00 hour
2. Downstream leg:
Distance = 1.00 mile
Speed = (b + r) = (2.00 + 1.00) = 3.00 mi/h
Time = Distance / Speed = 1.00 mile / 3.00 mi/h = 0.33 hours
To find the total travel time, we need to add the time taken for both the upstream and downstream legs:
Total travel time = Upstream time + Downstream time = 1.00 hour + 0.33 hours = 1.33 hours
Therefore, the travel time for the woman is 1.33 hours, corresponding to option (D).