MATH SOLVE

5 months ago

Q:
# The tanker continues to leak 720 gal/h after the first 8 hours. If the tanker originally contained 25,000 gal of oil, approximately how many more hours will elapse in the worst case before all of the oil has leaked? In the best case?

Accepted Solution

A:

Answer:It will take approximately 5 hours for all the oil to leak.Step-by-step explanation:The tanker continues to leak 720 gal/h after the first 8 hours. This means that the volume it has leaked after 8 hours is 720Γ8 = 5760 gallons.Let us assume that the rate follows an arithmetic progression such that at every 8 hours, 5760 gallons of oil. The first term of the sequence would be original volume of oil contained in the tank. This means that the first term is 25000 gallons. After 8 hours, the volume left would be 25000 - 5760= 19240 gallons.The common difference would be -5760 gallons since the volume is decreasing.When the volume becomes 0, that would be the final volume of the the tank when all the oil is leaked.For arithmetic progression,Tn = a+(n-1)dn = time it will take for the entire volume to leak offd = -5760Tn = 0a = 250000 = 25000 + (n-1) -57600 = 25000 -5760n + 57605760n = 25000 +5760= 30760n = 30760/5760 = 5.32Approximately 5 hours