Question

card 9
before a plane goes on a flight, it needs fuel from a refueling truck. this graph shows the amount of fuel in each vessel as it is pumped from the refueling truck to the plane.
graph of fuel volume (l) vs. time passed (min.) with two lines: one for refueling truck (decreasing) and one for plane (increasing)
which statement is true?
a. the relationship between time and volume of fuel in the refueling tank is proportional.
b. both the plane and the refueling truck start with no fuel.
c. the fuel in the refueling tank decreases at the same rate that the fuel in the plane increases.
d. the refueling truck started with less fuel than the plane.

Explanation:

Step1: Analyze Option A

A proportional relationship has a graph that passes through the origin \((0,0)\) and is a straight line. The refueling truck's graph starts at a positive fuel volume (since it's above the origin on the y - axis) and decreases linearly. So the relationship between time and its fuel volume is not proportional (because it doesn't pass through \((0,0)\) in the sense of a proportional relationship where \(y = kx\) with \(x = 0,y = 0\)). So A is false.

Step2: Analyze Option B

The plane's graph starts at \(0\) fuel (since it starts at the origin on the y - axis), but the refueling truck's graph starts at a positive fuel volume (it has fuel before time starts). So they don't both start with no fuel. B is false.

Step3: Analyze Option C

The fuel from the refueling truck is pumped into the plane. The rate of decrease of fuel in the truck should be equal to the rate of increase of fuel in the plane (because the fuel that leaves the truck is the same as the fuel that enters the plane, assuming no spillage). The graphs are straight lines (linear), so the slope of the truck's graph (rate of decrease) and the slope of the plane's graph (rate of increase) are equal in magnitude (since one is decreasing and one is increasing, but the amount of fuel transferred per unit time is the same). So C is true.

Step4: Analyze Option D

The refueling truck's graph starts at a higher fuel volume (on the y - axis) than the plane's (which starts at \(0\)). So the truck started with more fuel, not less. D is false.

Answer:

C. The fuel in the refueling tank decreases at the same rate that the fuel in the plane increases.