A ship traveled 150 km with the current, and then turned around and traveled back, spending 5h and 30 min on its trip. find the speed of the current if the speed of the ship in still water is 55 km/hour.

150=(55-c)(5.5-t)

5.5-t=150/(55-c)

-t=(150-302.5+5.5c)/(55-c)

t=(152.5-5.5c)/(55-c)

150=(55+c)t using t found about

150=(55+c)(152.5-5.5c)/(55-c)

8250-150c=8387.5-302.5c+152.5c-5.5c^2

5.5c^2=137.5

c^2=25

c=5

So the current is 5mph.

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alokdubeyvidyaatech alokdubeyvidyaatech · Answer 2 · 2022-03-08T13:04:18+01:00

The speed depends on distance and time. The speed of the current is 5 km/hr.

What is the speed?

The speed is defined as the total distance traveled by an object per unit time interval.

Given that the speed s of the ship in still water is 55 km/hr. the total distance is 150 km and the total time taken by the ship to cover the distance of 150 km with current and then turned around and traveled back, is 5 hr 30 min.

Let's consider that the speed of the current is c. Now, there will be two situations,

First is when the sheep travel with current and both are in the same direction. The total traveling speed will be,

[tex]S = s + c[/tex]

[tex]S = 55 +c[/tex]

The second one is when the ship travels without current and both are in opposite directions. The total traveling speed will be,

[tex]S' = s-c[/tex]

[tex]S' = 55-c[/tex]

Now the total traveling time is given as below.

[tex]5.5 \;\rm hr = \dfrac {D}{S} + \dfrac {D}{S'}[/tex]

[tex]5.5 = \dfrac {150}{55+c} + \dfrac {150}{55-c}[/tex]

[tex]1.1 = \dfrac {30}{55+c} + \dfrac {30}{55-c}[/tex]

[tex]1.1 (55+c)(55-c) = 30 (55+c ) +30 (55-c)[/tex]

[tex]1.1 (55^2 -c^2) = 30 (55+c+55-c)[/tex]

[tex]1.1(3025-c^2) =3300[/tex]

[tex]c^2 = \dfrac {27.5}{1.1}[/tex]

[tex]c^2 = 25[/tex]

[tex]c = 5 \;\rm km/hr[/tex]

Hence we can conclude that the speed of the current is 5 km/hr.

To know more about the speed, follow the link given below.

https://brainly.com/question/12759408.