This is a absolute value word problem that I had trouble with. Could anyone tell me how to solve it?

Question

a rainstorm begins as a drizzle, builds up to a heavy rain, and then drops back to a drizzle. The rate r (in inches per hour) at which it rains is given by the function r=-0.5|t-1|+0.5 where t is the time (in hours). for how long does it rain and when does it rain the hardest?

Answer 1

The graph of y = -0.5 l t l is an inverted "V-shaped" graph with highest point when t = 0 and y = 0.  

 

To obtain the graph of r = -0.5 l t - 1 l + 0.5, translate the graph of                           y = -0.5 l t l one unit to the right and 0.5 units upward.  The highest point on this graph occurs when t = 1 and r = 0.5.

 

Maximum rate of rainfall = 0.5 inches/hr

 

The rain stops when r = 0.  So,  -0.5 l t - 1 l + 0.5 = 0

 

                                                    l t - 1 l = 1

 

                                                     t - 1 = 1 or t - 1 = -1

 

                                                     t = 2 or t = 0

 

t > 0, so the rain stops when t = 2 hours