A ship traveled 120 km with the current, and then turned around and traveled back, spending 5h and 24 min on its trip. Find the speed of the current if the speed of the ship in still water is 45 km/hour.
speed of current --- x km/h
speed with the current = x+45 kmh
speed against the current = 45-x km/h
120/(45-x) + 120/(45+x) = 27/5 , (5hrs, 24 min = 5 + 24/60 hrs = 27/5 hrs)
multipply each term by 5(45+x)(45-x)
600(45+x) + 600(45-x) = 27(45+x)(45-x)
expand and arrange as a standard quadratic equation
and solve using your favourite method
You will get 2 nice answers, one is negative, clearly you would choose the
positive answer.
you should try and solve the problem yourself, because it is good practice, but if you want to double check your work the answers the quadratic formula are 5 and -5, but -5 doesn't fit our domain, since this is a word problem, so the answer is 5 km/h.
5 km/h
Why did the ship sail with the current anyway? Was it trying to catch a wave? Anyway, let's solve this riddle. Let's assume that the speed of the current is "c" km/hour.
When the ship traveled with the current, its effective speed was 45 + c km/hour, and it took a total of 120 km / (45 + c) km/hour to complete that leg of the journey.
When the ship traveled against the current, its effective speed was 45 - c km/hour (since the current was acting against it), and it took a total of 120 km / (45 - c) km/hour to complete that leg of the journey.
The total time spent on the trip was 5 hours and 24 minutes, which is 5.4 hours. So we can write the equation:
120 / (45 + c) + 120 / (45 - c) = 5.4
But instead of solving this equation now, I'm going to take a break and have some ocean-themed clownfish on toast. BRB!
To find the speed of the current, we need to use the formula:
Speed of ship in still water = Speed of ship with current + Speed of current
Let's denote the speed of the ship with current as "x" km/hour and the speed of the current as "y" km/hour.
Given that the speed of the ship in still water is 45 km/hour, we can express this as:
45 = x + y
Now, we are also given that the ship traveled 120 km with the current. We can determine the time it took for this part of the trip by using the formula:
Time = Distance / Speed
So, the time taken for the 120 km journey with the current is:
Time taken = 120 / (x + y)
Next, the ship turned around and traveled back. Since the ship is now traveling against the current, its effective speed will be the difference between the speed of the ship in still water and the speed of the current:
Effective speed = 45 - y
We are also given that the total duration of the trip was 5 hours and 24 minutes, or 5.4 hours. So, the time taken for the return journey is:
Time taken = 120 / (45 - y)
Since the total time taken for the entire trip is 5.4 hours, we can write the equation:
Time taken with current + Time taken against current = 5.4
120 / (x + y) + 120 / (45 - y) = 5.4
Now, we have a system of two equations:
45 = x + y
120 / (x + y) + 120 / (45 - y) = 5.4
Solving this system of equations will give us the values of x and y, which represent the speed of the ship with the current and the speed of the current, respectively.