40 miles is a long way from home if you were on foot. If I were to draw separate lines to N/S/W/E compass points 40 miles out in my AO, I would not be looking forward to a walk of this distance.
I can walk 4-1/2 miles in just over an hour (70 minutes) on pavement/good terrain with good proper shoes (not dress style) however I could not keep this pace up more then 2, maybe 3 hours tops on a good day without fatigue setting in and my speed dropping substantially. If your pace drops down to 3 miles an hour, do the math and you will see that a 30 mile walk can be 10 hours for more. Also keep in mind, even walking requires regular training. There is a local walking charity event here that is 30 kms (18 miles) in length and every year hundreds of "fit" people drop out due to .
I really suggest the maps and only the carry the essential, meaning cutting the map(s) to include your possible routes only. Alternatively save some offline Google Maps to your iPhone as every block or 1/4 mile saved by shortcutting through parks, shopping complexes etc can make a big difference when your hoofing it.
Good advice on the expectations to maintain for walking out. Most people only walk at 1.5 to 2 mph. If they press they are prone to "sore feet / ankles, sore shin muscles etc" and once you have get sore feet or shinsplints your chances of speeding up get slim without risking considerable, possibly demoralizing, pain and significant injury.
I wouldn't be too quick to cut down maps. Savings tend to be insignificant and the maps themselves are a resource. If you treat them to make them water resistant they are potential ground sheets, insulation, tinder. Rolled they are splints. That, and you never know where you might end up during an emergency. People have been diverted fifty miles and more by industrial accidents, bridges going down, etcetera.
Also it pays to have updated forestry service and topo maps of the area. Road maps often leave a lot out and the difference between being stuck and a minor inconvenience is sometimes in the details.
If hard-copy maps get bulky any full-service copy shop can provide useful services like changing scale, printing maps on both sides of a sheet, and printing on waterproof and tear resistant Mylar or Tyvek sheeting.
Depending on how hard-core you want to go you might get them printed on Tyvek or silk, and have it stitched into a jacket.