We can write the equation to solve this problem as:

#(72 + h)/(160 + h) = 0.560#

Where #h# is the number of consecutive hits need.

Solving for #h# gives:

#color(red)((160 + h)) xx (72 + h)/(160 + h) = color(red)((160 + h)) xx 0.560#

#cancel(color(red)((160 + h))) xx (72 + h)/color(red)(cancel(color(black)(160 + h))) = (color(red)(160) xx 0.560) + (color(red)(h) xx 0.560)#

#72 + h = 89.6 + 0.560h#

#-color(red)(72) + 72 + h - color(blue)(0.560h) = -color(red)(72) + 89.6 + 0.560h - color(blue)(0.560h)#

#0 + (1 - color(blue)(0.560))h = 17.6 + 0#

#0.44h = 17.6#

#(0.44h)/color(red)(0.44) = 17.6/color(red)(0.44)#

#(color(red)(cancel(color(black)(0.44)))h)/cancel(color(red)(0.44)) = 40#

#h = 40#

You will need #color(red)(40)# consecutive hits to move your batting average from 0.450 to 0.560