Which is faster A small boat can travel 7 ftsec in still wat

Which is faster? A small boat can travel 7 ft/sec in still water and wants to cross a 150 ft wide river that flows southwards with a water current of 3 ft/sec. It can point the craft directly East and drift with the current OR it can go slightly North to counter the current so as to end up going directly East. What is the resulting speed for each case their respective times to cross the river?

Solution

given the small boat speed =7ft/sec

speed of still water =3ft/sec

distance to be covered is 150ft

if goes in east then speed of still water get added so net resultant speed =7+3=10ft/sec

time taken to cross the river will be=150/10=15sec

if goes in north then speed of still water opposes the motion so net resultant speed =7-3=4ft/sec

time taken to cross the river will be =150/4=37.5 sec

so going towards east is faster since it takes less time