AlgebraHardDistance at which two fares are equal
Algebra practice question
One taxi company charges a $3 pick-up fee plus $2 per kilometre. A second company charges an $8 pick-up fee plus $1.50 per kilometre. For a trip of how many kilometres do the two companies charge the same fare?
Answer: 10
Set the fares equal: 3 + 2d = 8 + 1.5d. Subtract 1.5d: 3 + 0.5d = 8. Subtract 3: 0.5d = 5, so d = 10. Check: both fares are $23.
Common wrong answers
- If you answered 5
- 5 is the difference in pick-up fees (8 − 3); divide it by the difference in rates (0.5) to get the distance.
- If you answered 22
- 22 is (8 + 3)/0.5, adding the fees instead of subtracting them.
- If you answered 2.5
- 2.5 is 5 / 2, dividing by one rate instead of by the difference of the rates.
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