Respuesta :
Answer:
The speed of current is 5 miles per hour.
Step-by-step explanation:
Given:
In 6 hours a boat, traveling with the current, covers 20 more mi than in 10 hours, traveling against the current.
If the speed of the boat in still water is 15 mph.
Now, to find the speed of the current.
Let the speed of current be [tex]x.[/tex]
So, the speed of the boat going with current = [tex]x+15.[/tex]
And, the speed of the boat going against current = [tex]15-x.[/tex]
Let the distance travelled against the current be [tex]y.[/tex]
So, the distance travelled with the current = [tex]y+20.[/tex]
As, the time is given with the current = 6 hours.
And, the time against the current = 10 hours.
Now, to get the distance of boat travelled with the current:
[tex]Distance=speed\times time[/tex]
[tex]y+20=(x+15)\times 6[/tex]
[tex]y+20=6x+90[/tex]
Subtracting 20 on both sides we get:
[tex]y=6x+70[/tex]
Subtracting 6[tex]x[/tex] on both sides we get:
[tex]y-6x=70[/tex] .......( 1 )
Now, to get the distance of boat travelled against the current:
[tex]y=(15-x)\times 10[/tex]
[tex]y=150-10x[/tex]
Adding 10[tex]x[/tex] on both sides we get:
[tex]y+10x=150[/tex] .......( 2 )
Now, by using elimination method we subtract equation ( 1 ) from equation ( 2 ):
[tex]y+10x-(y-6x)=150-70[/tex]
[tex]y+10x-y+6x=80[/tex]
[tex]16x=80[/tex]
Dividing both sides by 16 we get:
[tex]x=5[/tex].
Therefore, the speed of current is 5 miles per hour.
