Question

A water tank holds 1,200 gallons but is leaking at a rate of 5 gallons per week. A second water tank holds 1,500 gallons but is leaking at a rate of 9 gallons per week. After how many weeks will the amount of water in the two tanks be the same?

Answer 1

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.

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,

=
`(Difference in the water level in tanks)/(Difference in the rate of leaking of water in tanks)`

=
`(300)/(4)`

= 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.