15. A sailboat moves at the speed of 30 km an hour with no one in the boat. The speed of the boat decreases by a quantity that varies as the cube root of the number of passengers who board the boat. With twenty–seven passengers on board it moves at 3 km an hour. How many passengers should board the boat so that it stops moving (approx.)?

• let z is a quantity by which the speed decreases.
  z=k(n)^1/3.
  n is the number of passengers.
  so speed =30-z
  speed =30-k(n)^(1/3)
  given that 30-k(27)^(1/3)=3
  solving it..we get k=9..
  To stop it ...30-9(n)^(1/3)=0
  n=37 so no. of passengers is 37..
• 10 years agoHelpfull: Yes(30) No(6)
• let the decrease be (x)*(no.of passengers)^1/3
  now for 27 passengers decrease=3km/h
  therefore 3=x*(27)^1/3...x=9
  therefore to stop the boat
  decrease needed=30 km
  thus, 9*(no.of passengers)^1/3=30
  no.of passengers=(30/9)^3..=37
• 10 years agoHelpfull: Yes(6) No(2)
• to reduce 3 km we need more 3^3 people...so in total 54 people
• 10 years agoHelpfull: Yes(1) No(9)