African elephants weigh approximately 13,000 pounds. They eat about 340 pounds of food per day and need nearly 26 gallons of water per day. If a herd of 22 elephants found 163,000 pounds of grasses in a section of savanna grasslands and a watering hole with 10,000 gallons of water, would the elephants run out of water or food first? How long could the herd stay before they run out of that item? If the elephants arrived on March 18th, on what day would they have to begin looking for a new spot?

The elephant herd would run out of water first in about 17.5 days.  They would have enough grass forage to last for about 21.8 days.  If the herd arrived at this location on March 18, they would need to begin looking for a new spot on April 4.  
To solve these questions, you need to figure out the needs of the entire herd and how long the area can sustain those needs.  
Each elephant eats 340 pounds of food/day.  340 pounds/day times 22 elephants means the entire herd consumes 7480 pounds/day.  There are 163,000 pounds available, so 163,000 pounds divided by 7480 pounds/day equals 21.8 days worth of food for the entire herd.
Each elephant drinks 26 gallons of water/day.  26 gallons/day times 22 elephants means the entire herd drinks 572 gallons/day.  There are 10,000 gallons available, so 10,000 gallons divided by 572 gallons/day equals 17.5 days worth of water for the entire herd.
Using March 18 as day 1 because that is when they begin to eat and drink in the new area, April 4 is the 18th (since that is technically day 17 and a half) day.  On that day the elephants are out of water and need to move.