Every minute, the herd travels 1/10 of a mile. And every minute, the stray travels 1/6 of a mile.
18. It took the stray 1/12 of an hour to catch up. Note that, if the stray ran for 5 miniutes, the distance it would cover would have been (R * T) = (1/6)mi/min * 5 min = 5/6 mile.
19. Note that, in the five minutes it took the stray to catch up, the herd traveled R * T = x = (1/10) mi/min * 5 min = x = 1/2 mile
20. Note that, if the stray ran 5/6 of a mile, the herd must have covered (5/6 - 1/2) = 1/3 of a mile while the stray stood still. To see why this is so, note that the herd travels (1/3) of a mile while the stray rests, and then travels another (1/2) mile in the five minutes the stray takes to catch up. So..... (1/3)mi + (1/2)mi = (5/6) mi. And that's how far the stray ran in the five minutes. In essence, the stray makes up (1/3) of a mile in 5 minutes. And this is so because his rate of (1/6)mi/min is being "retarded" by the (1/10)mi/min that the herd is traveling. So, his "efffective" rate is just (1/6 - 1/10) = 1/15mi/min. And multiplying this by 5 min = 1/3 mi.
So our Equation in this part is: (1/6 -1/10)t = d where t is the time it takes the stray elephant to catch the herd once it starts running and d is the distance the herd traveled while the stray stood still.
So
(1/6 - 1/10)mi/min *(5)min = 1/3 mi
(1/15)mi/min * (5 min) = 1/3 mi.
