A car travelled at 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 value of x.
Explanation
Time = \(\frac{\text{distance}}{\text{speed}}\)
t\(_1\) = \(\frac{(2x + 13) }{67.5}\) and t\(_2\) = \(\frac{(5x - 20) }{72}\)
Total time = t\(_1\) + t\(_2\) = 90mins = 1.5hrs
\(\frac{(2x + 13) }{67.5}\) + \(\frac{(5x - 20) }{72}\) = 1.5
multiply through by the LCM of 67.5 and 72
72(2x + 3) + 67.5(5x - 20) = 1.5(67.5)(72)
144x + 936 + 337.5x - 1350 = 7290
144x + 337.5 = 7290 + 1350 - 936
481.5x = 7704 (after collecting like terms)
x = \(\frac{7704}{481.5}\) = 16