Answer:
- The speed of the boat in still water is 8 miles per hour.
- The speed of the current is 4 miles per hour.
Solution:
We know the distance formula,
[tex]Distance=\frac{speed}{time}[/tex]
[tex]\Rightarrow Speed=Distance\times Time[/tex]
As boat travelled 240 miles downstream in 20 hours,
speed=[tex]\frac{240}{20} =12[/tex] miles per hour.
As boat travelled 240 miles upstream in 60 hours,
speed=[tex]\frac{240}{60} = 4[/tex] miles per hour.
Let the speed of boat in still water be x and the speed of current be y.
So, the equations formed are: [tex]x+y=12[/tex](downstream) --- (a) and [tex]x-y=4[/tex](upstream). --- (b)
On solving, (a)
[tex]\Rightarrow x=12-y[/tex] --- (c)
Substituting (c) in (b), we get [tex]12-y-y=4[/tex]
[tex]\Rightarrow 12-2y=4 \Rightarrow 12-4=2y \Rightarrow 8=2y \Rightarrow \frac{8}{2}=y[/tex]
Therefore, y=4 --- (d)
On substituting (d) in (a) we get,
[tex]x+4=12 \Rightarrow x=12-4 \Rightarrow x=8[/tex]
Therefore, x=8
Hence, Speed of boat in still water= 8 miles per hour and speed of current is 4 miles per hour.
