A hot-air balloon is 140 ft140 ft above the ground when a motorcycle (traveling in a straight line on a horizontal road) passes directly beneath it going 60 mi divided by hr60 mi/hr (88 ft divided by s88 ft/s). if the balloon rises vertically at a rate of 6 ft divided by s6 ft/s, what is the rate of change of the distance between the motorcycle and the balloon 10 seconds10 seconds later? let x be the horizontal distance from the balloon to the motorcycle, y be the vertical distance from the balloon to the road, and z be the distance between the motorcycle and the balloon. write an equation relating x, y, and z. nothing differentiate both sides of the equation with respect to t. left parenthesis nothing right parenthesis startfraction dx over dt endfraction plus left parenthesis nothing right parenthesis startfraction dy over dt endfraction equals left parenthesis nothing right parenthesis startfraction dz over dt endfraction dx dt+ dy dt= dz dt the rate of change of the distance between the motorcycle and the balloon after 10 seconds10 seconds is about nothing ▼ ft. ft. ft cubed divided by s. ft3/s. ft squared divided by s. ft2/s. ft divided by s. ft/s. (round to two decimal places as needed.)