$39.$ THINK This problem compares the U$.$K$.$ gallon with the U$.$S$.$ gallon, two nonSI units for volume. The interpretation of the type of gallons, whether U$.$K$.$ or U$.$S$.,$

affects the amount of gasoline one calculates for traveling a given distance.

EXPRESS If the consumption rate is R $($miles$/$gallon$),$ then the amount of gasoline

$($gallons$)$ needed for a trip of distance d $($miles$)$ would be

$($miles$)($gallons$).($miles$/$gallon$)$

d V

R$=$

Since the car was manufactured in the U$.$K$.,$ the consumption rate is calibrated based

on the U$.$K$.$ gallon, and the correct interpretation should be $40$ miles per U$.$K$.$

gallon.$$ In the U$.$K$.,$ one would think of the gallon as the U$.$K$.$ gallon; however, in the

U$.$S$.,$ the word $$gallon$$ would naturally be interpreted as U$.$S$.$ gallon. Note also that

since $1$ U$.$K$.$ gallon $=4\mathrm{.}5460900$ L and $1$ U$.$S$.$ gallon $=3\mathrm{.}7854118$ L$,$ the relationship

between the two is

CHAPTER $15$

$1$ U$.$S$.$ gallon $1$ U$.$K$.$ gallon $(4\mathrm{.}5460900$ L$)1\mathrm{.}20095$ U$.$S$.$ gallons. $3\mathrm{.}7854118$ L

$==$

ANALYZE $($a$)$ The amount of gasoline actually required is

$750$ miles $18\mathrm{.}75$ U$.$K$.$ gallons $18\mathrm{.}8$ U$.$K$.$ gallons. $40$ miles$/$U$.$K$.$ gallon

V$==$

This means that the driver mistakenly believes that the car should need $18\mathrm{.}8$ U$.$S$.$

gallons.

$($b$)$ Using the conversion factor found above, this is equivalent to

$()1\mathrm{.}20095$ U$.$S$.$ gallons $18\mathrm{.}75$ U$.$K$.$ gallons $22\mathrm{.}5$ U$.$S$.$ gallons. $1$ U$.$K$.$ gallon

V $=$

LEARN A U$.$K$.$ gallon is greater than a U$.$S$.$ gallon by roughly a factor of $1\mathrm{.}2$ in

volume. Therefore, $40$ mi$/$U$.$K$.$ gallon is less fuel efficient than $40$ mi$/$U$.$S$.$ gallon. Given quantities $(10\%)$

Unknown quantities $(10\%)$

Sketch the situation given in the problem $(10\%)$

Principle$($s$)/$ Key idea$($s$)(10\%)$

Equations corresponding to key ideas $(10\%)$

Analytic solution $(20\%)$

Numeric solution $(15\%)$

Final Answer $(5\%)$

Unit check $(5\%)$

Number check $(5\%)$