Calculate Downstream Speed

Downstream speed is the sum of the speed of the boat in still water and the speed of the current: $v_{\text{down}} = v + u = 32 + 23 = 55$ km/h.

$v_{\text{down}} = 32 + 23 = 55 \text{ km/h}$

Calculate Upstream Speed

Upstream speed is the difference between the speed of the boat in still water and the speed of the current: $v_{\text{up}} = v - u = 32 - 23 = 9$ km/h.

$v_{\text{up}} = 32 - 23 = 9 \text{ km/h}$

Calculate Time Taken for Both Legs

Time taken to travel downstream: $t_{\text{down}} = \frac{495}{55} = 9$ hours. Time taken to travel upstream: $t_{\text{up}} = \frac{495}{9} = 55$ hours.

$t_{\text{down}} = 9 \text{ h}, \quad t_{\text{up}} = 55 \text{ h}$

Calculate Total Time

Sum the time taken for downstream and upstream journeys to get the total time: $T = t_{\text{down}} + t_{\text{up}} = 9 + 55 = 64$ hours.

$T = 9 + 55 = 64 \text{ hours}$