With math, sometimes you've got to dig a little deeper

Three men dig a ditch. Collectively, this activity takes them 18 hours. How much time would it take two men to dig the same ditch?

Room 24 solves a math word problem every day. I am proud to report that I am able to find (almost) every answer with relative ease prior to presenting my 4th graders with their daily math scenario.

Usually.

The problem above seemed pretty clear cut.

Until.

Until I TRIED to solve it. "Okay, Amy," (I'm a big self-talker), "3 men digging for 18 hours? So...divide. 3 into 18 is 6. So that means every man dug for 6 hours each. Wow! They must have been really tired." I checked the answer key.

Wrong.

What?!?!

Two frustrating hours of mulling (in between watching YouTube videos...have you seen the one where they're bottle-feeding a baby otter? So precious) and I still wasn't successful in finding another reasonable solution.

I posed the problem to my college-age daughter when I got home. "Wrong," I told her. "No...that HAS to be right," Sydney protested, quickly sketching her reasoning out on our refrigerator's dry erase board. I nodded. "That's what I got too," I admitted glumly. We were going to be forced to get out the big gun:  The Engineer. Unfortunately, the engineer lacks humility and was sure to rub our utter stupidity in our face.

"The answer is 9," Savannah announced over the phone before I'd barely finished reading her the problem. "How on earth can it possibly be nine," I growled, "That doesn't even REMOTELY make sense." "I'll call you back," Savannah sighed. Thirty seconds later, she had sent me a picture diagram. "First of all," I said to Sydney as we studied the illustration, "your's is cuter." "Thank you," Sydney murmured modestly. "What does this mean," I asked Sydney, Savannah's mathematical hieroglyphics were a jumble of meaningless figures.

The phone rang. "So...now do you understand," Savannah asked triumphantly.  "No," we shouted. "You have to SPLIT the hours of the third guy," Savannah explained slowly, as if to idiots. "We're not stupid, Savannah...your picture is," I spat. "I'll call you back," she sighed.

Thirty seconds later, we received another picture. "Your's is still cuter," I assured Sydney as we studied this up-dated version. "Ohhhh-hhhh..." we said, suddenly enlightened.

The phone rang. "Now do you get it," Savannah asked fearfully. "How did you know how to do that," I said, filled with wonderment. We could practically hear Savannah shrugging in Connecticut.

There was no WAY that my poor 4th graders were going to be able to solve this problem. I tried to skip it on my agenda board but they made me go back. A little challenge never hurt anyone, I reasoned. I watched them huddled over their little dry erase boards, shoulder hunched, markers flying. "We'll reveal on 3...2...1" I directed, facing sixteen solutions. "9," they shouted. Maybe I should dig ditches for a living.