Respuesta :
Answer:
The speed of boat in still water is 11 miles per hour
The speed of current is 10 miles per hour .
Step-by-step explanation:
Given as :
The distance cover by boat in downstream = [tex]d_1[/tex] = 147 miles
The time taken by boat in downstream trip = [tex]t_1[/tex] = 7 hours
The distance cover by boat in upstream = [tex]d_2[/tex] = 147 miles
The time taken by boat in upstream trip = [tex]t_2[/tex] = 147 hours
Let The speed of boat in still water = [tex]s_1[/tex] = x mph
And The speed of the current = [tex]s_2[/tex] = y mph
Now, According to question
Speed = [tex]\dfrac{\textrm Distance}{\textrm Time}[/tex]
For downstream
[tex]s_1[/tex] + [tex]s_2[/tex] = [tex]\dfrac{d_1}{t_1}[/tex]
or, x + y = [tex]\dfrac{147}{7}[/tex]
I.e x + y = 21 mph ..........1
For upstream
[tex]s_1[/tex] + [tex]s_2[/tex] = [tex]\dfrac{d_2}{t_2}[/tex]
or, x - y = [tex]\dfrac{147}{147}[/tex]
I.e x - y = 1 mph ..........2
Now, Solving Eq 1 and 2
I.e (x + y) + (x - y) = 21 + 1
Or, (x + x) + (y - y) = 22
Or, 2 x = 22
∴ x = [tex]\frac{22}{2}[/tex]
I.e x = 11 mph
So, speed of boat = x = 11 miles per hour
Again, put The value of x in Eq 2
So, x - y = 1 mph
I.e 11 - y = 1
∴, y = 11 - 1
I.e y = 10 mph
So, speed of current = y = 10 miles per hour
Hence The speed of boat in still water is 11 miles per hour , and The speed of current is 10 miles per hour . Answer
