Question

A worker accidentally spills some contaminant into a drum filled to the top with 10 gallons of water. He quickly grabs a hose and begins to pour in water to clear out the contaminant. The water flows through the hose at 2 gal/min. After ten minutes, his supervisor catches him and stops him. the worker claims he only spilled a small amount. The supervisor takes a reading and finds the concentration of the contaminant is 0.01lb/gal. How much did the worker spill?

Answer 1

After 10 minutes 10×2=20 gallons would be added to the 10 gallons of water that was in the drum, so, if there's no overflow, there will be 10+2×10=30 gallons in all. The concentration of contaminant is now found to be 0.01lb/gal, so in 30 gallons 0.3lb of contaminant would have been initially spilled into the drum.

(If the drum overflows as more water pours into it, all the contaminant would have been flushed out by displacement, because  the drum can only contain 10 gallons.)