NABTEB Mathematics 2024 Theory — Question 2
Question 2 of 13 from the National Business and Technical Examinations Board (NABTEB) Mathematics 2024 Theory paper, with the correct answer and a full explanation.
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2. A car travelled a distance of (2x+13)km at 67.5km/h and (5x−20)km at 72km/h. If the total time for the entire journey was 90 minutes, find the value of x.
Model answer
Time = Distance/Speed. Total time = 90 minutes = 1.5 hours. (2x+13)/67.5 + (5x−20)/72 = 1.5 Multiplying through by 540 (LCM of 67.5 and 72, since 540/67.5=8 and 540/72=7.5): 8(2x+13) + 7.5(5x−20) = 1.5×540 16x + 104 + 37.5x − 150 = 810 53.5x − 46 = 810 53.5x = 856 x = 16.
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