Two cars left the city for a suburb, 120 km away, at the same time. The speed of one of the cars was 20 km/hour greater than the speed of the other, and that is why it arrived at the suburb 1 hour before the other car. What is the speed of both cars.?
Slower car:
Faster car:
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Let the speed of the slower car be ( x ) km/hour and the speed of the faster car be ( x + 20 ) km/hour.
Using the formula: ( \text{speed} = \frac{\text{distance}}{\text{time}} )
For the slower car: ( \frac{120}{x} ) hours
For the faster car: ( \frac{120}{x+20} ) hours
Given that the faster car arrives 1 hour earlier:
( \frac{120}{x} = \frac{120}{x+20} + 1 )
Solving for ( x ): ( 120(x+20) = 120x + x(x+20) )
( 120x + 2400 = 120x + x^2 + 20x )
( x^2 + 20x - 2400 = 0 )
( (x - 40)(x + 60) = 0 )
( x = 40 ) or ( x = -60 )
Since speed cannot be negative, the speed of the slower car is 40 km/hour and the speed of the faster car is ( 40 + 20 = 60 ) km/hour.
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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
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