Why 5% Fewer Miles and 7% Better MPG Do Not Simply Add

Ada re-derives this chapter’s own numbers step by step, at full precision

ADA · CALCULATION AUDIT

Why 5% Fewer Miles and 7% Better MPG Do Not Simply Add

A fleet drives 3,000,000 miles a year at 8 MPG on $3.50 diesel, and route optimization promises 5% fewer miles and 7% better MPG for a reported $147,196 in annual fuel savings. It is tempting to read that as a 5 + 7 = 12% cut. But fuel burned is miles divided by MPG, so this audit carries every digit through and asks whether the true saving is that 12%, or the 11.2% the ratio actually yields.

Companion to the chapter Transportation and Vehicles — every number here comes from that chapter.

Ada: This section reports $147,196 in annual fuel savings from two improvements — 5% fewer miles and 7% better MPG. It is tempting to read that as a 5 + 7 = 12% cut, but fuel burned is miles divided by MPG, so the two effects combine as a ratio, not a sum. Let me carry the chapter’s own numbers through at full precision and check both the dollar figure and the fraction it really represents.

Baseline, from the given 3,000,000 miles at 8 MPG and $3.50/gallon:

• Gallons: 3,000,000 / 8 = 375,000 gallons
• Cost: 375,000 x 3.50 = $1,312,500

After optimization the mileage and efficiency both change:

• New miles: 3,000,000 x 0.95 = 2,850,000
• New efficiency: 8 x 1.07 = 8.56 MPG
• New gallons: 2,850,000 / 8.56 = 332,943.925... gallons (the chapter rounds this to 332,944)
• New cost: 332,943.925 x 3.50 = $1,165,303.74, which rounds to the chapter’s $1,165,304
• Savings: 1,312,500 - 1,165,303.74 = $147,196.26, matching the reported $147,196

Now the fraction that saving represents. Because both terms scale the same baseline, the new-over-old fuel ratio collapses to just the mileage and efficiency factors:

• Fuel ratio: 0.95 / 1.07 = 0.887850
• Savings fraction: 1 - 0.887850 = 0.112150 = 11.21%

So the true saving is 11.2%, not the 12% a naive 5% + 7% would suggest — the 0.8-point gap is exactly the interaction between driving fewer miles and burning less per mile. Reassuringly, 11.2% lands inside the chapter’s own “10-15% fuel savings” ROI band, so the worked example is self-consistent and, if anything, conservative. The design lesson: when a saving is a ratio of two improved quantities, add the percentages only to sketch a ceiling — commit the multiplicative figure to the ROI case, because that is the money the fleet actually keeps.

Every number above is taken from the chapter’s own material and re-derived step by step.