how far apart are they

Question

Three cities lie along a perfectly linear route: Springfield, Clarksville, and Allentown. Molly lives in Springfield and works in Allentown. She makes it to work using two gallons of gas in her car. Her friend Edgar lives in Allentown and works in Clarksville. It takes Edgar one gallon of gas to get to work. If Molly's car averages 26 miles per gallon, and Edgar's car averages 17 miles per gallon, about how far apart are Springfield and Clarksville?

Answer 1

Draw a diagram and label!

2 gal @ 26 mpg = 52 miles - distance between Springfield and Allentown

1 gal @ 17 mpg = 17 miles - distance between Allentown an Clarksville

 

How far is Clarksville from Springfield?

Answer 2

Assuming a left to right order of Springfield, Clarksville, and Allentown:

 

x = distance from Springfield to Clarksville

y = distance from Clarksville to Allentown

x + y = distance from Springfield to Allentown

 

2 gallons of gas from Springfield to Allentown at 26 miles per gallon ⇒

x + y = 2(26) miles = 52 miles

 

1 gallon of gas from Allentown to Clarksville at 17 miles per gallon ⇒

y = 1(17) miles = 17 miles

 

x = (x + y) - y = (52 - 17) miles = 35 miles

 

Distance from Springfield to Clarksville is 35 miles

Distance from Clarksville to Allentown is 17 miles

Distance from Springfield to Allentown is 52 miles