Question

A large barrel of oil is 1/4 full.Then for 7 1/2 minutes, oil is added to the barrel at a rate of 4.5 gallons per minute.Then for 6 1/2 minutes, some of the oil is removed at a rate of -3 1/2 gallons per minute.Is the barrel now more or less than 1/4 full?

Answer 1

Answer:

The barrel now is more than 1/4 full

Step-by-step explanation:

* A large barrel of oil is 1/4 full.

* Then for 7 1/2 minutes, oil is added to the barrel at a rate of

   4.5 gallons per minute.

* Then for 6 1/2 minutes, some of the oil is removed at a rate of

   -3 1/2 gallons per minute.

* We need to know The oil in the barrel now is more or less than

   1/4 full

* To know that calculate the quantity of oil added in the barrel and the

   quantity of oil removed from the barrel.

* If the quantity of oil add is greater than the quantity of oil removed

   then, the barrel is more than 1/4 full

* If the quantity of oil removed is greater than the quantity of oil

   added then, the barrel is less than 1/4 full

∵ The oil is added to the barrel at a rate of 4.5 gallons per minute

   for $7\frac{1}{2}$ minutes

∴ The quantity of oil add = 4.5 × 7.5 = 33.75 gallons

∵ The oil is removed from the barrel at a rate of -3.5 gallons per minute

   for $6\frac{1}{2}$ minutes

∴ The quantity of oil removed = -3.5 × 6.5 = -22.75 gallons

   The negative sign to know that this quantity is removed

∵ The quantity of oil add is greater than the quantity of oil removed

∴ The barrel now is more than 1/4 full