Math Word Problem

Question

The gas tank in a boat holds a total of 35 gallons. The boat travels 100 miles on 5 gallons of gas. If the tank is full at the beginning of the trip, write an equation that represents the change in the amount of gas in the tank.

Answer 1

100 miles/5 gallons = 20 miles per gallon or 20 mpg.

We will let d be the distance the boat has traveled and g be the gallons of gas used to travel that distance

g = d/20

The gallons remaining in the tank will be 35 - g or 35 - d/20.

Answer 2

The boat uses 1 / 20 or 0.05 gallon per mile (5 / 100)

t represents what is in the tank

t = 35 - 0.05m

Answer 3

d = rt

distance = rate of speed times time or mpg times tiime

100 = 100/5 = 20 mpg = 20 miles per gallon as the boat travels

for 35 gallons, the boat can travel 35x20 = 700 miles before having an empty tank

Gas in the tank = G = Full tank = 35 - miles traveled divided by mpg = 35 - M/20

G = 35- M/20 where G = gas in the tank, and M = miles the boat traveled, maximum miles = 700

change in the tank is the derivative of G:

G' = -1/20

or

G' = - 0.05 is an equation describing the change in gas gallons in the tank over one mile traveled. It's a constant, regardless how many miles traveled.

G' means each mile the boat travels, the amount of gas in the tank decreases by 20 gallons

(but then Obama B. graduated magna cum laude from Harvard, so he already knows the solution. Not too many math courses in Harvard Law School though. Odds are he didn't take any or many at Columbia either. Occidental in LA probably wanted an algebra class though, which covered this problem. Long time ago though. Math memories fade quickly.)