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

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 $\frac{mi}{hr}$

Total time taken ( T )= 10 hours

$T = \frac{D}{u - v} + \frac{D}{u +v}$

$10 = \frac{21}{u - 2} + \frac{21}{u + 2}$

$10 = \frac{42 u}{u^{2}-4 }$

$10 u^{2} - 42 u -40 = 0$

$u^{2} - 4.2 u - 4 = 0$

By solving above equation we get

u = 5 $\frac{mi}{hr}$

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

$T = \frac{D}{u + v}$

$T = \frac{21}{5 + 2}$

T = 3 hours

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