The velocity of a motor boat with respect to still water is $7m{s}^{-1}$  and velocity of water in a river is $3m{s}^{-1}$ . When the boat starts moving upstream a float was dropped from it. The boat travels 4.2 km and returns and reaches the float. The time taken by the boat to catch the float is

When the boat is in upstream. Relative velocity between boat and float is = 10 m/sec

The separation between them when boat moves 4.2 km is $S=V_{rel}t$

$V_{rel}\frac{d}{V_{boat}}=10\times \frac{4.2\times 1000}{7}$

= 6000 m

When the boat is in down stream, relative $v_{rel}=4m/\sec$  time taken to cover the separation distance 6000m is $t_1=\frac{6000}{4}=1500\sec =25\min$

Total time from starting of journey is

$T_e=25+\frac{d}{V_{boat}}$

$=25+\frac{4200}{7\times 60}=$

= 35 min