Question

It's 176 miles from Ayville to Bravotown. It's another 210 miles from Bravotown to Charlietown. Todd drives 30 miles faster from Bravotown to Charlietown than from Ayville to Bravotown. If his combined travel time is 7.4 hours, what are his average speeds?

Answer 1

(176/x) + (210/(x + 30)) = 7.4

176(x + 30) + 210x = 7.4x(x + 30)

880(x + 30) + 1,050x + 37(x² + 30x)

880x + 26,400 + 1,050x = 37x² + 1,110x

37x² - 820x - 26,400 = 0

x = (820 ± √(820² - 4(37)(-26,400)))/74

= (820 ± √4,579,600)/74

= (820 + 2,140)/74

= 2,960/74

= 40

40 mph from Ayville to Bravotown

70 mph from Bravotown to Charlietown.