Question

A boat travels between two riverside cities, A and B, located 21 miles apart. The river flows in the direction from A to B at 2 mph. The boat takes a total of 10 hours to make a round trip from A to B and back to A again. How long does it take the boat to make the one-way trip from A to B if the boats speed remailer constant relative to the speed of the river in each direction

Answer 1

The time taken by the boat to make the one-way trip from A to B = 3 hrs

Step-by-step explanation:

Distance between A & B = 21 mile

Velocity of river ( v ) = 2
`(mi)/(hr)`

Total time taken ( T )= 10 hours

`T = (D)/(u - v) + (D)/(u +v)`

`10 = (21)/(u - 2) + (21)/(u + 2)`

`10 = (42 u)/(u^(2)-4 )`

`10 u^(2) - 42 u -40 = 0`

`u^(2) - 4.2 u - 4 = 0`

By solving above equation we get

u = 5
`(mi)/(hr)`

The time taken by the boat to make the one-way trip from A to B

`T = (D)/(u + v)`

`T = (21)/(5 + 2)`

T = 3 hours

This is the time taken by the boat to make the one-way trip from A to B.