two automobiles start out at the same time from cities 595 km apart if the speed of one is 8 by 9 of the speed of the other and if they meet in 7 hours what is the speed of each

Dear student, let speed of 1st automobile = v , the speed of 2 nd automobile = 8v/9 . When they met , let the distance covered by automobile 1 = D1 . Distance covered by automobile 2 = D2 . D1+D2 = 595 km . As , time = distance / speed , 7 = D1/v = D2/(8v/9) = 9D2/8v . From these equations we get , D1 = 7v , D2 = 56v/9 . Substituting in D1 + D2 = 595 we get , 7v + 56v/9 = 595 . Which implies (63+56)v/9 = 595 . v = (595×9)/119 = 45 km/h . Speed of automobile 1 = v = 45km/h . Speed of automobile 2 = 8v/9 = 40km/h . Regards