Dona drove 300 miles north from San Antonio, mostly on the freeway. She usually averaged 55 mph, but an accident slowed her speed through Dallas to 15 mph. If her trip took 6 hours, how many miles did she drive at the reduced rate ?

Answer:The distance she took at reduce speed is 11.25  milesStep-by-step explanation:Given as :The Distance cover from San Antonio before accident = D miles The Distance cover after accident = ( 300 - D ) milesThe average speed before accident = 55 mphThe average speed after accident = 15 mph Total time for the journey = 6 hours Now, Time = [tex]\frac{Distane}{Speed}[/tex] ∴ [tex]\frac{D}{55}[/tex] + [tex]\frac{D - 300}{15}[/tex] = 6 Or, [tex]\frac{3 D + 11 ( 300 - D )}{165}[/tex] = 6Or,  [tex]\frac{3 D + 3300 - 11 D}{165}[/tex] = 6Or,  3300 - 8 D = 165 × 6Or,  3300 - 8 D = 990Or, 8 D = 2310∴       D = [tex]\frac{2310}{8}[/tex] = 288.75 milesThe distance travel at reduce speed = 300 - D                                                              = 300 - 288.75                                                              = 11.25  milesHence The distance she took at reduce speed is 11.25  miles