A swimmer heading directly across a river that is 200 m wide reaches the opposite bank in 6 min 40 s.During this swim,she is swept downstream 480 m.What is the speed of the current?
A)0.50 m/s
B)0.80 m/s
C)1.2 m/s
D)1.4 m/s
E)1.8 m/s

Question

Quizplus · Accepted Answer

Let's assume the speed of the swimmer in still water is v and the speed of the current is u.
Then, the swimmer's speed while swimming across the river would be (v^2 + u^2)^0.5, and the net velocity relative to the ground would be v - u.
We know that the swimmer covers the 200 m distance in 6 min 40 s (i.e., 400 seconds). So, we can write the following equation:
200 = (v - u) x 400
=> (v - u) = 0.5 m/s    ------ (Equation 1)
Also, we know that during this swim, the swimmer is swept downstream by 480 m. So, we can write the following equation:
480 = (v + u) x 400
=> (v + u) = 1.2 m/s    ------ (Equation 2)
Now, if we subtract Equation 1 from Equation 2, we get:
2u = 0.7 m/s
=> u = 0.35 m/s
Therefore, the speed of the current is 0.35 m/s.

A Swimmer Heading Directly Across a River That Is 200