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secondary 4 | E Maths
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Date Posted: 5 years ago
Views: 239
Let km represent kilometers.
Let h represent hours.
The car has an average speed of 600km/xh, while the plane has an average speed of 600km/(x - 11/2)h.
We know that the average speed of the plane is 220km/h faster than the car, so:
600km/xh + 220km/h = 600km/(x - 11/2)h
Let's remove the units to make it easier to expand out later:
600/x + 220 = 600/(x - 11/2)
Now, we multiplying both sides by x(x - 11/2):
600(x - 11/2) + 220x(x - 11/2) = 600x
Expand out:
600x - 3300 + 220x^2 - 1210x = 600x
We can remove "600x" from both sides:
220x^2 - 1210x - 3300 = 0
Dividing both sides by 110:
2x^2 - 11x - 30 = 0
Now, we factorise:
(2x - 15)(x + 2) = 0
x = 15/2 or x = -2
But since x is representing the number of hours, x = -2 is rejected.
The average speed of the car is therefore 600km/(15/2)h = 1200km/15h = 80km/h.
Let h represent hours.
The car has an average speed of 600km/xh, while the plane has an average speed of 600km/(x - 11/2)h.
We know that the average speed of the plane is 220km/h faster than the car, so:
600km/xh + 220km/h = 600km/(x - 11/2)h
Let's remove the units to make it easier to expand out later:
600/x + 220 = 600/(x - 11/2)
Now, we multiplying both sides by x(x - 11/2):
600(x - 11/2) + 220x(x - 11/2) = 600x
Expand out:
600x - 3300 + 220x^2 - 1210x = 600x
We can remove "600x" from both sides:
220x^2 - 1210x - 3300 = 0
Dividing both sides by 110:
2x^2 - 11x - 30 = 0
Now, we factorise:
(2x - 15)(x + 2) = 0
x = 15/2 or x = -2
But since x is representing the number of hours, x = -2 is rejected.
The average speed of the car is therefore 600km/(15/2)h = 1200km/15h = 80km/h.
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We need to convert the word problem into an equation using the relation
Distance = Speed x Time
and the other two modified expressions of the same equation for speed and time.
Remember that the value of x which we extract at the end must make sense i.e. x must be positive since x represents the time taken for the journey (even x = 0 does not really make much sense here).
Distance = Speed x Time
and the other two modified expressions of the same equation for speed and time.
Remember that the value of x which we extract at the end must make sense i.e. x must be positive since x represents the time taken for the journey (even x = 0 does not really make much sense here).
Date Posted:
5 years ago
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