A boat rescued people drowning in a river during a flood, with maximum of 5 people at a time 7 people were holding a rock in middle of water flow. The boat arrives and picks 5 of them and left 2 people holding the rock. When the boat began to travel upstream, 2 people holding the rock, left hold of it and start flowing with the water flow. The boat travels 2 km upstream, left the 5 people, turned about and caught with the 2 people drowning. how long will it take the boat to reach those 2 people?
Take, speed of boat w.r.t. to still water =10m/s
Speed of water flow =2m/s

Explanation

For upstream motion of boat:
Relative velocity w.r.t. to water flow =10-2=8m/s
Distance traverlled =2 km =2000m
Time taken, `t_(1)=(2000)/(8)=250s`
For downstream motion of 2 people
Distance moved by them in 250s=`2xx250=500m`
Distance between the boat after it turned about and 2 people in the water `=2000+500=2500m`
This distance is to be covered by the boat with its own velocity (w.r.t. to still water) because the velocity of the water flow is shared by both (both and the 2 people in water)
`therefore` Time taken `t_(2)=(2500)/(10)=250s`
Total time taken to reach them, `t=t_(1)+t_(2)`
`=(250+250)s`
=500s
`=(500)/(60)=8.33` mins.