Respuesta :
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
Speed of the boat in still water is 87.5 km/hr and speed of the current is 17.5 km/hr.
What is downstream?
A boat moving along the direction of the stream is called downstream. The net speed of the boat in this case is called downstream speed.
What is upstream?
A boat moving in the direction opposite to the direction of the stream is called upstream. 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,
[tex]420=(x+y)4[/tex]
⇒ [tex]x+y=105[/tex] and
the equation 2 as, [tex]420=(x-y)6[/tex]
⇒ [tex]x-y=70[/tex]
On adding equations 1 and 2 we get, [tex]2x=175[/tex]
⇒ [tex]x=87.5[/tex]
On substituting the value of x in equation 1, we get
⇒ [tex]87.5+y=105[/tex]
⇒ [tex]y=17.5[/tex]
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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