every day daniel drives 100 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 ( 2 x ) 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 ?
"let ' s test x = 4 . . . . on sunday , daniel drove 100 miles at 4 miles / hour . d = ( r ) ( t ) 100 = ( 4 ) ( t ) 100 / 4 = 25 = t it takes 25 hours to drive home on monday , daniel drove the first 32 miles at ( 2 ) ( 4 ) = 8 miles / hour and the rest of the way ( 68 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 ) 68 = ( 2 ) ( t ) 68 / 2 = 34 = t it takes 34 hours for the second part total time to drive home on monday = 4 + 34 = 38 hours we ' re asked by what percent 38 hours is greater than 25 hours . 38 / 25 = 1.52 , so it is 52 % greater . e"
multiply(divide(subtract(add(divide(32, 2), multiply(subtract(100, 32), 2)), 100), 100), const_100)