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.

Question

Quizplus · Accepted Answer

Let the speed of the river be x mi/h. When the woman rows upstream, her speed relative to the river is (2-x) mi/h. Similarly, when she rows downstream, her speed relative to the river is (2+x) mi/h.
Using the formula distance = speed x time, we can write two equations:
1) Distance upstream = 1 mile
(2-x)T = 1
2) Distance downstream = 1 mile
(2+x)T = 1
where T is the time taken for each journey (upstream and downstream).
Solving for T:
T = 1/(2-x) = 1/(2+x)
2-x = 2+x
2x = 2
x = 1
Substituting x=1 into one of the equations above:
T = 1/(2-1) = 1 hour
Therefore, the total travel time is 2 hours (1 hour upstream + 1 hour downstream). The best choice is D.

A River 100 Mile Wide Flows with a Constant Speed of 1