this is how I'd set it up:
405/20 = 243/x
this means the mpg (miles / gallons) for 1 situation is the same as the mpg for the other situation (because the rate is the same)
then just cross multiply and solve:
405x=243*20 or 405x=4860 or x = 12
he would need 12 gallons of gas for 243 miles