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Chapter 3: Problem 68

A Nile cruise ship takes \(20.8 \mathrm{h}\) to go upstream from Luxor to Aswan, a distance of \(208 \mathrm{km},\) and \(19.2 \mathrm{h}\) to make the return trip downstream. Assuming the ship's speed relative to the water is the same in both cases, calculate the speed of the current in the Nile.

Short Answer

Expert verified
Answer: The approximate speed of the current in the Nile is 0.807 km/h.

Step by step solution

01

Define Variables

Let's define the variables. Let's say \(s\) is the speed of the ship relative to the water, and \(c\) is the speed of the current in the Nile. We are given that the time taken by the ship to go upstream is \(20.8\ \mathrm{h}\) and downstream is \(19.2\ \mathrm{h}\), with the total distance covered in each direction being \(208\ \mathrm{km}\).
02

Set up Equations for Upstream and Downstream Travel

When the ship is traveling upstream, it goes against the current. So the effective speed in this case will be \((s-c)\ \mathrm{km/h}\). Using the distance formula, we have: $$(s-c) \times 20.8 = 208$$ When the ship is traveling downstream, it goes along with the current. So the effective speed in this case will be \((s+c)\ \mathrm{km/h}\). Using the distance formula, we have: $$(s+c) \times 19.2 = 208$$
03

Solve the Equations for Ship Speed and Current Speed

Now we need to solve the equations for \(s\) and \(c\). First, let's solve the first equation for \(s\): $$s = \frac{208}{20.8} + c$$ Then substitute this expression into the second equation: $$\left(\frac{208}{20.8} + c + c\right) \times 19.2 = 208$$ Simplify the equation and solve for \(c\): $$\left(10 + 2c\right) \times 19.2 = 208$$ $$2c = \frac{208}{19.2} - 10$$ $$c = \frac{1}{2}\left(\frac{208}{19.2} - 10\right)$$
04

Calculate the Speed of the Current

Now we can find the value of \(c\): $$c = \frac{1}{2}\left(\frac{208}{19.2} - 10\right) \approx 0.807\ \mathrm{km/h}$$ The speed of the current in the Nile is approximately \(0.807\ \mathrm{km/h}\).

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