A hybrid car can travel 40 miles per gallon. Approximately how many gallons of fuel will the car need to travel 20 km?

[1 mile = 1.6 km]

a.) 0.3
b.) 0.8
c.) 2.5
d.) 3.2

Question

A hybrid car can travel 40 miles per gallon. Approximately how many gallons of fuel will the car need to travel 20 km?

[1 mile = 1.6 km]

a.) 0.3
b.) 0.8
c.) 2.5
d.) 3.2

mathmale · Answer

You may find it interesting and helpful to watch your units of measurement carefully.  We want to know the number of gallons of gas needed to travel a certain distance, when the fuel economy (miles per gallon) and the distance to be traveled  are given.

Fuel econ:$$\frac{ 40 mi }{ 1gal }$$and distance:  20 km.

mathmale · Answer

It'd be easier to convert 20 km into miles than to convert 40 mi / 1 gal into Km / liter (metric system).

mathmale · Answer

So, let's keep $$\frac{ 40 mi }{ 1gal }$$  as the fuel economy rating of the vehicle, anc convert 20 km into miles.

mathmale · Answer

1 mile is approx. 1.6 Km, and 1 Km is approx. 0.621 mile.
Deriving a km->miles conversion factor from the first identity will enable us to eliminate the unit of measurement "Km" in favor of "miles."  $$If 1mile=1.6 km, $$then the appropriate conversion factor is $$\frac{ 1mile }{ 1.6 km }.$$

mathmale · Answer

Application:  convert 20Km into miles.

Multiply 20 Km by $$\frac{ 1mile }{ 1.6 km }.$$

mathmale · Answer

We get the following:$$\frac{ 1mile }{ 1.6Km }*20 Km$$

mathmale · Answer

The unit of measurement Km cancels from numerator and denominator, leaving $$\frac{ 20 miles }{ 1.6}\approx 12.5 miles$$

mathmale · Answer

Note that dividing the distance, 12.5 miles, by the fuel economy, $$\frac{ 40 miles }{ 1gallon}$$

mathmale · Answer

produces a quantity with units "gallons," as required.  Thus, we calculate$$\frac{ 12.5miles }{ \frac{ 40 miles }{ gallon } }=\frac{ 12.5 }{ 40 }gallons$$

mathmale · Answer

Reduce that to lowest terms.  The answer will be a fraction of a gallon.

anonymous · Answer

12.5/40 = 0.3125

anonymous · Answer

@mathmale

mathmale · Answer

Neffy:  0.3125 what?  Important to include units of measurement.

anonymous · Answer

@mathmale 0.3 gallons. So that is the answer?

mathmale · Answer

Yes, very good.  That's "approximately" how much fuel would be needed.

anonymous · Answer

@mathmale  okay thank you!

mathmale · Answer

My great pleasure!  Good luck and Happy New Year!

anonymous · Answer

@mathmale You too!