Answer:
The speed of the current in a river is 6 miles per hour.
Step-by-step explanation:
Given:
A boat moves at 20 miles/hour in still water and takes 3 hours to travel 78 miles downstream.
Now, to determine the average speed of the current in river.
Let the speed of boat in still water be [tex]x\ miles\ per\ hour.[/tex]
Boat moves in still water at = 20 miles/hour
So, [tex]x=20\ miles\ per\ hour.[/tex]
And the speed of the stream be [tex]y\ miles/hr.[/tex]
So, speed of downstream = [tex](x+y)\ miles/hr[/tex]
Now, the speed of upstream = [tex](x-y)\ miles/hr[/tex]
As given:
Distance = 78 miles.
Time = 3 hours.
Speed of downstream = [tex]\frac{Distance}{Time}[/tex]
Speed of downstream = [tex]\frac{78}{3}=26\ miles\ per\ hour[/tex]
As speed of downstream is taken as [tex](x+y)\ miles/hr[/tex]
Thus,
Speed of downstream = [tex](x+y)\ miles/hr[/tex]
[tex]26=x+y[/tex]
(As we see above [tex]x=20\ miles\ per\ hour.[/tex])
⇒ [tex]26=20+y[/tex]
Subtracting both sides by 20 we get:
⇒ [tex]6=y[/tex]
⇒ [tex]y=6.[/tex]
So, speed of the stream = 6 miles per hour.
Therefore, the speed of the current in a river is 6 miles per hour.
