Question

it takes a ship 4 hours to sail 420 km with the current and 6 hours against the current. Find the speed of the ship in still water and the speed of the current. somebody help me please :-

Answer 1

Speed of the boat in still water = 87.5 km/hr and Speed of the current = 17.5 km/hr.

What are downstream and upstream?

A boat is said to go downstream if it is moving along the direction of the stream. The net speed of the boat, in this case, is called downstream speed.

A boat is said to go upstream if it is moving in the direction opposite to the direction of the stream. The net speed of the boat, in this case, is called upstream speed.

For the given situation,

Let’s assume the speed of the boat in still water be x km/hr

And the speed of the current be y km/hr.

So, the speed of the boat in downstream = (x+y) km/hr.

The speed of the boat in upstream = (x−y) km/hr

The formula to find the speed is Distance = Speed×Time

Distance traveled = 420 km

Time taken to sail in downstream = 4 hours

Time taken to sail in upstream = 6 hours

Now, according to the given situation, we have the equation 1 as,

$420=(x+y)4$

⇒ $x+y=105$ and

the equation 2 as, $420=(x-y)6$

⇒ $x-y=70$

On adding equations 1 and 2 we get, $2x=175$

⇒ $x=87.5$

On substituting the value of x in equation 1, we get

⇒ $87.5+y=105$

⇒ $y=17.5$

Hence we can conclude that the speed of the boat in still water is 87.5 km/hr and speed of the current is 17.5 km/hr.

Learn more about downstream and upstream here

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Answer 2

Answer:

The speed of the ship is 87.5 km/hr and the speed of the current is 17.5 km/hr.

Step-by-step explanation:

4:420 with current

6:420 against current

so we can do

420/4 and 420/6

105 and 70

2s - 0c = 105

s = 87.5 km/hour

87.5 + c = 105

c = 17.5 km/hour