Respuesta :
Answer:
The speed of current is 7 miles per hour
Step-by-step explanation:
Given as :
The distance cover by boat in downstream = D = 147 miles
The distance cover by boat in upstream = d = 147 miles
The time taken in downstream trip = T = 7 hours
The time taken in upstream trip = t = 21 hours
Let The speed of boat in still water = x mi/h
And The speed of current = y mi/h
The speed in downstream = S = (x + y) mi/h
The speed in upstream = s = (x - y) mi/h
Now, According to question
∵ Distance = speed × time
For downstream
D = S × T
Or, 147 miles = (x + y) mi/h × 7 hours
i.e 7 (x + y) = 147
Or, x + y = [tex]\dfrac{147}{7}[/tex]
∴ x + y = 21 ........A
For upstream
d = s × t
Or, 147 miles = (x - y) mi/h × 21 hours
i.e 21 (x - y) = 147
Or, x - y = [tex]\dfrac{147}{21}[/tex]
∴ x - y = 7 .......B
Now, Solving equations A and B
So, (x + y) + (x - y) = 21 + 7
Or, (x + x) + (y - y) = 28
Or, 2 x + 0 = 28
∴ x = [tex]\dfrac{28}{2}[/tex]
i.e x = 14 miles per hour
The speed of boat in still water = x = 14 mi/h
Now, putting the value of x into eq B
So, y = x - 7
Or, y = 14 - 7
i.e y = 7 miles per hour
The speed of current = y = 7 mi/h
Hence, The speed of current is 7 miles per hour . Answer
