1 answer
(click or scroll down)
Make a sketch to see that:
distance covered between bounce 1 and 2 = 2(10)(3/5) <--- once up, then down
distance covered between bounce 2 and 3 = 2(10)(3/5)^2
distance covered between bounce 3 and 4 = 2(10)(3/5)^2
....
total distance = 10 + [2(10)(3/5) + 2(10)(3/5)^2 + 2(10)(3/5)^3 + .... ]
the part in [ .. ] is an infinite series with a = 20(3/5) and r = 3/5
distance = 10 + a/(1-r)
leaving the actual arithmetic to you, let me know what you get