The Amount Of Gasoline Used By A Car Varies Jointly As The Distance Travelled And…
The amount of gasoline used by a car varies jointly as the distance travelled and the square root of the speed. Suppose a car used 25 liters on a 100 kilometer- trip at 100 kph, about how many liters will it use in a on a 1000 km. trip at 64 kph?
Answer:
To solve this problem, we can use the concept of joint variation.
Let’s define the variables:
– Let G represent the amount of gasoline used (in liters)
– Let D represent the distance traveled (in kilometers)
– Let S represent the speed (in kilometers per hour)
According to the problem, the amount of gasoline used (G) varies jointly as the distance traveled (D) and the square root of the speed (S). Mathematically, we can express this relationship as:
G = k * D * √S
where k is a constant of variation.
We are given the following information:
– For a 100 kilometer trip at 100 kph, the car used 25 liters of gasoline.
Using this information, we can plug in the values into the equation to find the value of k:
25 = k * 100 * √100
25 = k * 100 * 10
25 = k * 1000
k = 25 / 1000
k = 0.025
Now that we have the value of k, we can use it to find the amount of gasoline used for a 1000 kilometer trip at 64 kph:
G = 0.025 * 1000 * √64
G = 0.025 * 1000 * 8
G = 200 liters
Therefore, the car will use about 200 liters of gasoline for a 1000 kilometer trip at 64 kph.
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