The house hunting story.

Like a best friend, math can provide an enlightening advice anywhere in our daily routine. For example, a number of years ago it has helped us pinpoint the optimal home location.

For over a year we have been trying to find the hidden gem, looking across ten different suburbs with one child in a car seat and another in my belly. Every weekend started optimistically with googling out the best route through that weekend's Open Houses. But toward the end of Sunday our mood shifted from the excitement of expectations to disappointment and exhaustion. Shall we buy close to my husband's work, my work, our son's daycare, in the middle? A trendy downtown loft closer to our jobs or a cozy suburban house closer to the day care? Did we consider switching the day care? God forbid! Day care that provided us with the excellent full day coverage and great resources for our kid, day care that it took us a year to get in: switching it was not an option.

We looked everywhere, getting more confused with each new neighborhood we discover. Then one day, while waiting in-between Open Houses with my son napping in his car seat, it struck me that I can narrow down the desired location just by doing some math. Location, Location, Location. Optimal Home Location. Commute was a killer of our family time: two hours per day combined for all three of us. Where should we live in order to minimize our combined family commute? What is our Optimal Home Location?

With my son asleep in the back, I drew a sketch of the daily commutes to work and daycare for everyone in the family.

Commute route #1 (My husband): Home->Day Care->Work1->Home

Commute route #2 (Me): Home->Work2->DayCare->Home

Commute route #3 (our son): Home->Day Care->Home

Then, denoting our optimal home location with (x, y) unknowns, I tried to see how to find the minimum of the sum of our commutes. Assuming that we buy close to my husband's work, I substituted (x,y) with his work location and computed the combined miles. The I did the same for my work, our son's day care and a location in the middle of the triangle. Looking at the results it was clear that our combined commute minimum is reached when the house is closer to the daycare. Interestingly, this was not at all the center of a triangle in-between all the points we commute to (Day Care, Work1, Work2), as I initially assumed. Contemplating about it, it did make sense - we drove to the day care three times a day (each adult drives once and our toddler son once) and to our offices only once.

Rescued by math suggestion and narrowing down our search space to five mile radius around the day care, we quickly compromised on a house that soon became a home of our dreams. We saved time and money, and improved our well-being. As a bonus, kids are thrilled to have friends close-by. No wonder scientific studies directly link commute length to happiness. Commuting to work has been reported to be the least enjoyable activity (even ahead of house chores) in the survey performed by Princeton scientists. Another European study shockingly claimed that people commuting to work 1 hour each way should earn 40% more in salary to be as satisfied with their lives as non-commuters.

Generalizing my computation for every family, I created a free Family Relocation Tool: Optimal Home Location Tool. Enter your commute pattern and see how you can save your traffic frustration, gain more family time, lower your carbon footprint and improve your well-being.

Top image by Houstonian, distributed under CCL.