a man cycling along the road noticed that every 12 minutes a bus overtakes him and every 4 minutes he meets an oncoming bus . if all buses and the cyclist move at a constant speed , what is the time interval between consecutive buses ?
"let ' s say the distance between the buses is d . we want to determine interval = \ frac { d } { b } , where b is the speed of bus . let the speed of cyclist be c . every 12 minutes a bus overtakes cyclist : \ frac { d } { b - c } = 12 , d = 12 b - 12 c ; every 4 minutes cyclist meets an oncoming bus : \ frac { d } { b + c } = 4 , d = 4 b + 4 c ; d = 12 b - 12 c = 4 b + 4 c , - - > b = 2 c , - - > d = 12 b - 6 b = 6 b . interval = \ frac { d } { b } = \ frac { 6 b } { b } = 6 answer : b ( 6 minutes ) ."
divide(subtract(12, divide(12, divide(add(4, 12), subtract(12, 4)))), const_1)