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Vlada [557]
4 years ago
6

Running at maximum speed, it takes a boat times as long to go 10 miles upstream as it does to go 10 miles downstream. If the cur

rent is 4 mph, find the speed of the boat in still water.
Physics
1 answer:
Greeley [361]4 years ago
7 0

Note: <em>The question states the time to go upstream is a number of times (not explicitly written) the time to go downstream. We'll assume a general number N</em>

Answer:

\displaystyle v_b=\frac{N+1}{N-1}(4\ mph)

Explanation:

<u>Relative Speed</u>

If a boat is going upstream against the water current, the true speed of motion is v_b-v_w, being v_b the speed of the boat and v_w the speed of the water. If the boat is going downstream, the true speed becomes v_b+v_w.

The question states the time to go upstream is a number of times N (not explicitly written) the time to go downstream. The speed of an object is computed as

\displaystyle v=\frac{x}{t}

Where x is the distance traveled and t the time taken for that. The time can be computed by

\displaystyle t=\frac{x}{v}

If t_u is the time for the upstream travel and t_d is the time for the downstream travel, then

t_u=Nt_d

Siince the same distance x= 10 miles is traveled in both cases:

\displaystyle \frac{10}{v_b-v_w}=N\frac{10}{v_b+v_w}

Simplifying and rearrangling

v_b+v_w=N(v_b-v_w)

Operating

v_b+v_w=Nv_b-Nv_w

Solving for v_b

\displaystyle v_b=\frac{N+1}{N-1}v_w

If\ N=2,\ v_w=4\ mph

\displaystyle v_b=\frac{3}{1}(4)=12\ mph

If N=3

\displaystyle v_b=\frac{4}{2}v_w=2(4)=8\ mph

We can use the required value of N to compute the speed of the boat as explained

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