a man cycling along the road noticed that every 10 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 10 minutes a bus overtakes cyclist : \ frac { d } { b - c } = 10 , d = 10 b - 10 c ; every 4 minutes cyclist meets an oncoming bus : \ frac { d } { b + c } = 4 , d = 4 b + 4 c ; d = 10 b - 10 c = 4 b + 4 c , - - > b = 7 c / 3 , - - > d = 12 b - 12 b * 3 / 7 = 48 / 7 b . interval = \ frac { d } { b } = \ frac { 48 / 7 b } { b } = 48 / 7 answer : e ( 48 / 7 minutes ) ."
divide(subtract(10, divide(10, divide(add(4, 10), subtract(10, 4)))), const_1)