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A driver starts a journey with 25 gallons in the tank of his car. The car burns 5 gallons for every 100 miles. Assuming that the amount of gasoline in the tank decreases linearly,
a) write a linear function that relates the number of gallons G left in the tank after a journey of x miles.
b) What is the value and meaning of the slope of the graph of G?
c) What is the value and meaning of the x intercept?
Solution to Problem 8:
a) If 5 gallons are burnt for 100 miles then (5 / 100) gallons are burnt for 1 mile. Hence for x miles, x * (5 / 100) gallons are burnt. G is then equal to the initial amount of gasoline decreased by the amount gasoline burnt by the car. Hence
G = 25 - (5 / 100) x
b) The slope of G is equal to 5 / 1000 and it represent the amount of gasoline burnt for a distance of 1 mile.
c) To find the x intercept, we set G = 0 and solve for x.
25 - (5 / 100) x = 0
x = 500 miles : it is the distance x for which all 25 gallons of gasoline will be burnt.
Calculating travel times
3. Suppose your office is 30 miles away from home. You have to get there at 8 a.m., and know that the traffic is moving at 60 miles per hour. To find out the time you should leave home, translate the word problem into an equation: time taken = distance divided by the rate of travel. So t (time) = d (distance)/r (rate), and t=30/60. So t=1/2 or half an hour. To reach the office at 8 a.m., you should leave at 7:30 a.m.
"The Man Who Can't Be Moved"
Going back to the corner where I first saw you
Gonna camp in my sleeping bag I'm not gonna move
Got some words on cardboard, got your picture in my hand
Saying, "If you see this girl can you tell her where I am?"
Some try to hand me money, they don't understand
I'm not broke – I'm just a broken-hearted man
I know it makes no sense but what else can I do?
How can I move on when I'm still in love with you?
a) write a linear function that relates the number of gallons G left in the tank after a journey of x miles.
b) What is the value and meaning of the slope of the graph of G?
c) What is the value and meaning of the x intercept?
Solution to Problem 8:
a) If 5 gallons are burnt for 100 miles then (5 / 100) gallons are burnt for 1 mile. Hence for x miles, x * (5 / 100) gallons are burnt. G is then equal to the initial amount of gasoline decreased by the amount gasoline burnt by the car. Hence
G = 25 - (5 / 100) x
b) The slope of G is equal to 5 / 1000 and it represent the amount of gasoline burnt for a distance of 1 mile.
c) To find the x intercept, we set G = 0 and solve for x.
25 - (5 / 100) x = 0
x = 500 miles : it is the distance x for which all 25 gallons of gasoline will be burnt.
Calculating travel times
3. Suppose your office is 30 miles away from home. You have to get there at 8 a.m., and know that the traffic is moving at 60 miles per hour. To find out the time you should leave home, translate the word problem into an equation: time taken = distance divided by the rate of travel. So t (time) = d (distance)/r (rate), and t=30/60. So t=1/2 or half an hour. To reach the office at 8 a.m., you should leave at 7:30 a.m.
"The Man Who Can't Be Moved"
Going back to the corner where I first saw you
Gonna camp in my sleeping bag I'm not gonna move
Got some words on cardboard, got your picture in my hand
Saying, "If you see this girl can you tell her where I am?"
Some try to hand me money, they don't understand
I'm not broke – I'm just a broken-hearted man
I know it makes no sense but what else can I do?
How can I move on when I'm still in love with you?