# Algebra

1.A motorcycle has a reserved fuel of 0.5 liter which can be used if it's 3-liter fuel tank is about to be emptied. The motorcycle consumes at most 0.5 liter fuel for every 20 km of travel.
a. What mathematical statement represents the amount of fuel that would be left in the motorcycle's fuel tank after traveling a certain distance if it's tank is full at the start of travel?
b. Suppose the motorcycle's tank is full and it travels a distance of 55 km, about how much fuel would be left in the tank?
c. If the motorcycle travels a distance of 130 km with its tank full, would the amount of fuel in its tank be enough to cover the given distance? Explain why?
2. A bus and a car left a place at the same time traveling in opposite direction. After 2 hours, the distance between them is at most 350 km.
a. What mathematical statement represents the distance between the two vehicles after 2 hours? Define the variables used.
b. What could be the average speed of each vehicle in kilometers per hour?
c. If the car travels at a speed of 70 kilometers per hour, what could be the maximum speed of the bus?
d. If the bus travels at a speed of 70 kilometers per hour, is it possible that the car's speed is 60 kilometers per hour? Explain or justify your answer.
e. If the car's speed is 65 kilometers per hour, is it possible that the bus speed is 75 kilometers per hour? Explain or justify your answer.

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1. 1a. Fr = 3 - 0.5L/20km * d.
Fr = 3 - 0.025d.

Fr = Fuel remaining in liters.
d = Distance traveled in km.

b. Fr = 3 - 0.025*55 = 1.625 Liters.

c. No. When d equals 130 km, Fr is negative which means the tank empties before 130 km is reached.
The max distance can be calculated by setting Fr to zero and solving for d:

Fr = 3 - 0.025d = 0.
0.025d = 3.
d = 120 km, max.

2a. D = Dc - Db.
Dc: East.
Db:West(negative).

b. V = 0.5*350km/2h = 87.5 km/h(Assuming Dc = Db).

c. D = Vc*t - Vb*t = 350 km.
70*2 - Vb*2 = 350.
-2Vb = 350-140 = 210.
Vb = -105 km/h = 105 km/h, West.

d. D = Vc*2 - (-70*2) = 350.
2Vc + 140 = 350.
2Vc = 210.
Vc = 105 km/h, East.

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2. tabular method

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