A Nile cruise ship takes 21.7 h to go upstream from Luxor to Aswan, a distance of 208 km, and 20.3 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.
(Vs-Vc)t1 = 208 km.
(Vs+Vc)t2 = 208 km.
Vs*t1-Vc*t1 = 208
Vs*t2+Vc*t2 = 208
Eq1: 21.7Vs - 21.7Vc = 208
Eq2: 20.3Vs + 20.3Vc = 208
Multiply Eq1 by 20.3 and Eq2 by 21.7 and
add the Eqs:
440.51Vs - 440.51Vc = 4222.4
440.51Vs + 440.51Vc = 4513.6
Sum: 881.02Vs = 8736
Vs = 9.92 km/h = Velocity of the ship.
In Eq1, replace Vs with 9.92 and solve for Vc(Velocity of the current.).
To solve this problem, we will use the concept of relative velocity.
Let's assume the speed of the ship in still water be V and the speed of the current be S.
When the ship is going upstream (against the current):
Speed of the ship relative to the ground = Speed of the ship in still water - Speed of the current
So, the time taken to cover the distance of 208 km upstream is given as:
21.7 hours = 208 km / (V - S)
When the ship is going downstream (with the current):
Speed of the ship relative to the ground = Speed of the ship in still water + Speed of the current
So, the time taken to cover the distance of 208 km downstream is given as:
20.3 hours = 208 km / (V + S)
We can solve these two equations simultaneously to find the values of V (speed of the ship in still water) and S (speed of the current).
Let's solve it step by step:
Step 1: Set up the equations:
21.7 = 208 / (V - S)
20.3 = 208 / (V + S)
Step 2: Rearrange the equations:
21.7(V - S) = 208
20.3(V + S) = 208
Step 3: Simplify the equations:
21.7V - 21.7S = 208
20.3V + 20.3S = 208
Step 4: Multiply both equations by their respective denominators to eliminate fractions:
21.7V - 21.7S = 208 * 21.7
20.3V + 20.3S = 208 * 20.3
Step 5: Simplify further:
21.7V - 21.7S = 4513.6
20.3V + 20.3S = 4218.4
Step 6: Add the two equations together to eliminate S:
(21.7V - 21.7S) + (20.3V + 20.3S) = 4513.6 + 4218.4
21.7V + 20.3V = 8732
Step 7: Simplify further:
42V = 8732
Step 8: Solve for V by dividing both sides by 42:
V = 8732 / 42
V = 207.71 km/h
Step 9: Substitute the value of V back into one of the original equations, let's use the first one:
21.7 = 208 / (V - S)
21.7 = 208 / (207.71 - S)
Step 10: Solve for S:
21.7 (207.71 - S) = 208
21.7 * 207.71 - 21.7S = 208
21.7S = 21.7 * 207.71 - 208
S = (21.7 * 207.71 - 208) / 21.7
Solving this equation gives us:
S = 1.12 km/h
So, the speed of the current in the Nile is approximately 1.12 km/h.
To calculate the speed of the current in the Nile, we can use the formula:
Speed of the current = (speed upstream - speed downstream)/2
Let's first calculate the speed upstream.
Distance = Speed x Time
208 km = Speed upstream x 21.7 h
Speed upstream = 208 km / 21.7 h
Speed upstream = 9.58 km/h
Now, let's calculate the speed downstream.
208 km = Speed downstream x 20.3 h
Speed downstream = 208 km / 20.3 h
Speed downstream = 10.24 km/h
Finally, we can calculate the speed of the current.
Speed of the current = (10.24 km/h - 9.58 km/h) / 2
Speed of the current = 0.66 km/h
Therefore, the speed of the current in the Nile is approximately 0.66 km/h.