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

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.

Try

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. Calculate this case.

Observe

It is tempting to read that as a 5 + 7 = 12% cut. Check shows this.

Explain

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 twochanging terms, multiply their retained fractions rather than adding their percentage savings. Check confirms it.

See the relationship before changing it

The figure reads from left to right. The blue input is miles reduction. The middle card names the page’s rule. The green output is annual saving. The arrow matters: change the input, apply the rule once, then read the result with its unit.

Walk the arrow. Miles fall while MPG rises, so the two changes combine as a ratio.

Derive the baseline in four named moves

1. 1

   Name the input. The chapter baseline is 5 %.

2. 2

   Name the relationship. saving = 1,312,500 x (1 - (1 - miles cut)/1.07)

3. 3

   Substitute with units. 1,312,500 x (1 - 0.95/1.07) = 147,196.26 USD

4. 4

   Read the result. Keep the unit beside the value, then use the result only inside the technical boundary below.

Predict, then change miles reduction

Try Predict how annual saving responds when miles reduction moves. Calculate miles reduction; compare annual saving with that prediction.

Miles reduction

5 %

Chapter baseline

Annual saving

Observe Return to 5 %. Recheck annual saving with miles reduction at its chapter value.

Explain Miles fall while MPG rises, so the two changes combine as a ratio.

Check yourself

What should you do before trusting a moved-slider result?

Answer: Predict its direction, apply the displayed relationship, keep the units, and compare the reset value with the chapter’s worked baseline.

What does this small model leave out?

Answer: Only miles reduction moves here. The annual saving calculation excludes field effects listed below.

Honesty note. The annual saving result holds miles reduction as the only changing input. It is not a field prediction.

Technical boundaries

Outside the fixed “Why 5% Fewer Miles and 7% Better MPG Do Not Simply Add” arithmetic are traffic changes, route mix, idling, vehicle load, tyre condition, or interaction between mileage and fuel-efficiency interventions; “Why 5% Fewer Miles and 7% Better MPG Do Not Simply Add” therefore reports only its named fixtures.

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.