16. A Nile cruise ship takes 21. 0 h to go upstream from Luxor to Aswan, a distance of 208 km, and 19.8 h to make the return trip downstream. Assuming the ship’s speed relative to the water is the same in both cases, calculate the average speed of the current in the Nile. Answer in : ______ km/h
(v+c)19.8 = (v-c)21
and
(v+c)19.8 = 208
To calculate the average speed of the current in the Nile, we need to understand the concept of relative speed.
Let's assume the speed of the ship is "S" km/h, and the speed of the current is "C" km/h.
When the ship is moving upstream, its effective speed will be the difference between its speed and the speed of the current. So, the speed upstream is (S - C) km/h.
Similarly, when the ship is moving downstream, its effective speed will be the sum of its speed and the speed of the current. So, the speed downstream is (S + C) km/h.
We are given that the ship takes 21.0 hours to go upstream from Luxor to Aswan (208 km) and 19.8 hours to make the return trip downstream.
Using the formula speed = distance / time, we can set up the following equations:
For the upstream journey:
(S - C) km/h = 208 km / 21.0 h
For the downstream journey:
(S + C) km/h = 208 km / 19.8 h
To find the average speed of the current, we need to solve these equations simultaneously.
Dividing the two equations, we get:
(S - C) / (S + C) = (208 km / 21.0 h) / (208 km / 19.8 h)
Simplifying this equation, we can cross-multiply to get:
(19.8 h)(S - C) = (21.0 h)(S + C)
Expanding, we have:
19.8S - 19.8C = 21.0S + 21.0C
Collecting like terms:
21.0C - 19.8C = 21.0S - 19.8S
1.2C = 1.2S
C = S
From this equation, we can see that the speed of the current (C) is equal to the speed of the ship (S). This indicates that the current has no effect on the average speed of the ship.
Therefore, the average speed of the current in the Nile is 0 km/h.