Answer:
The time taken by the boat to make the one-way trip from A to B = 3 hrs
Explanation:
Distance between A & B = 21 mile
Velocity of river ( v ) = 2 [tex]\frac{mi}{hr}[/tex]
Total time taken ( T )= 10 hours
[tex]T = \frac{D}{u - v} + \frac{D}{u +v}[/tex]
[tex]10 = \frac{21}{u - 2} + \frac{21}{u + 2}[/tex]
[tex]10 = \frac{42 u}{u^{2}-4 }[/tex]
[tex]10 u^{2} - 42 u -40 = 0[/tex]
[tex]u^{2} - 4.2 u - 4 = 0[/tex]
By solving above equation we get
u = 5 [tex]\frac{mi}{hr}[/tex]
The time taken by the boat to make the one-way trip from A to B
[tex]T = \frac{D}{u + v}[/tex]
[tex]T = \frac{21}{5 + 2}[/tex]
T = 3 hours
This is the time taken by the boat to make the one-way trip from A to B.
