How to model a word problem with a system of equation?

Question

Ben's truck contains 20 gallons of gas when full and uses 1 gallon to go 18 miles on the highway. Sarah's car contains 15 gallons of gas when full and uses 1 gallon to go 26 miles on the highway. If he starts with a full tank of gas, how much gas will Ben have after driving 40 miles? If she starts with a full tank of gas, how far can Sarah drive before she runs out of gas? If they both start with a full tank of gas and drive side-by-side on the highway, how far will they have driven when they have the same amount of gas in their car?

Answer 1

40/18=2 4/18=2 2/9 gallons used

20-2 2/9=17 7/9 gallons left

 

26*15=390 miles is how far Sarah can drive before she runs out of gas

 

20-(x/18)=15-(x/26)

multiply both sides by the LCM of 18 and 26 which is 234

234(20-[x/18])=234(15-[x/26])

4680-13x=3510-9x

4680-3510=13x-9x

1170=4x

x=1170/4

x=292.5 miles is how far they must drive to have the same amount of gas in their cars

check: 292.5/18=16.25 gallons, 20-16.25=3.75 gallons left

          292.5/26=11.25 gallons, 15-11.25=3.75 gallons left