This is basically a variation of the "how long till the trains collide" scenario.
At one hour, 1/2 + 1/3rd of the lawn (4/6) will be done, leaving 1/3 of the lawn.
At one hour and 10 minutes, 4/6 of the lawn plus 4/6th of the remaining 1/3rd will be done, or 16/18.
At one hour, 10 minutes plus 1 minute 36/54 + 12/54 + 4/54 of the lawn will be done, for 52/54 of the lawn. The remaining 2/54 of the lawn will be 4/6 done in half a minute, leaving you with roughly 1 hr 12 minutes.