Every day Daniel drives 96 miles back from work. On Sunday, Daniel drove all the way back from work at a constant speed of x miles per hour. On Monday, Daniel drove the first 32 miles back from work at (2x) miles per hour, and the rest of the way at (x/2) miles per hour. The time it took Daniel to drive back from work on Monday is longer than the time it took him to drive back from work on Sunday by what percent? Choose one
A) 10 %  B) 20 %  C) 30 %  D) 40 %  E) 50 %

Rationale: "let ' s test x = 4 . . . . on sunday , daniel drove 96 miles at 4 miles / hour . d = ( r ) ( t ) 96 = ( 4 ) ( t ) 96 / 4 = 24 = t it takes 24 hours to drive home on monday , daniel drove the first 32 miles at ( 2 ) ( 4 ) = 8 miles / hour and the rest of the way ( 64 miles ) at 4 / 2 = 2 miles / hour d = ( r ) ( t ) 32 = ( 8 ) ( t ) 32 / 8 = 4 = t it takes 4 hours for the first part d = ( r ) ( t ) 64 = ( 2 ) ( t ) 64 / 2 = 32 = t it takes 32 hours for the second part total time to drive home on monday = 4 + 32 = 36 hours we ' re asked by what percent 36 hours is greater than 32 hours . 36 / 32 = 1.5 , so it is 50 % greater . e"
Answer: E