Theory question 102
Algebraic ExpressionsA car travelled a distance of (2x + 13) km at 67.5 km/h and (5x − 20) km at 72 km/h. If the total time for the entire journey was 90 minutes, find the velue of x.
Show the model answer
Model answer
Time = distance ÷ speed, and 90 minutes = 1.5 h
(2x + 13)/67.5 + (5x − 20)/72 = 1.5
Multiply by 1080: 16(2x + 13) + 15(5x − 20) = 1620
107x − 92 = 1620 ⇒ 107x = 1712 ⇒ x = 16
Explanation
Change 90 minutes to hours before forming the equation.