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Question
Car A travels ‘x’ km for every litre of petrol, while car B travels (x + 5) km for every litre of petrol.
- Write down the number of litres of petrol used by car A and car B in covering a distance of 400 km.
- If car A uses 4 litres of petrol more than car B in covering 400 km. write down an equation, in A and solve it to determine the number of litres of petrol used by car B for the journey.
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Solution
Let car A travel x km per litre and car B travel (x+5) km per litre.
Petrol used by car A: `400/x ` litres
Petrol used by car B: `400/(x+5)` litres
Given:
Car A uses 4 litres more petrol than car B.
`400/x = 400/(x+5) + 4`
Multiply both sides by x(x + 5):
400(x + 5) = 400x + 4x(x + 5)
400x + 2000 = 400x + 4x2 + 20x
4x2 + 20x − 2000 = 0
Divide by 4:
x2 + 5x − 500 = 0
(x − 20) (x + 25) = 0
x = 20
Petrol used by car B = `400/(x+5)`
`=400/25`
= 16
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