Respuesta :
75 weeks takes for the amount of water in the two tanks be the same, if a 1200 gallons water tank leaking rate of 5 gallons per week and 1500 gallons water tank leaking rate of 9 gallons per week.
Step-by-step explanation:
       The given is ,
          First water tank holds 1200 gallons and leaking at a rate of 5 gallons per week.
         Second water tank holds 1500 gallons and leaking at a rate of 9 gallons per week.
Step:1
      The difference in the water level in tanks,
           = Second tank - First tank
           = 1500 - 1200
           = 300 gallons
Step:2
     The difference in the rate of leaking of water in tanks,
        = Rate of leaking of second tank - rate of leaking of first tank
        = 9 - 5
        = 4 gallons per week
Step:3
     Weeks takes for the two tanks are same level of water,
           = [tex]\frac{Difference in the water level in tanks}{Difference in the rate of leaking of water in tanks}[/tex]
           = [tex]\frac{300}{4}[/tex]
           = 75 weeks
Step:4
    Check for solution,
    Water at the first tank after 75 weeks,
         = Total capacity - Amount of water leaked at 75 weeks
         = 1200 - ( 5 × 75)
         = 825 gallons
     Water at the second tank after 75 weeks,
         = Total capacity - Amount of water leaked at 75 weeks
         = 1500 - ( 9 × 75)
         = 825 gallons
      Water at the first tank after 75 weeks = Water at the second tank after 75 weeks,
        825 gallons = 825 gallons
Result:
    75 weeks takes for the amount of water in the two tanks be the same, if a first water tank holds 1200 gallons at a leaking rate of 5 gallons per week and second water tank holds 1500 gallons at a leaking rate of 9 gallons per week.
