Question

Ray has found that his new car gets 31 miles per gallon on the highwayand 26 miles per gallon in the city. He recently drove 285 miles on 10gallons of gasoline. How many miles did he drive on the highway? Howmany miles did he drive in the city

Answer 1

`Highway = 155\ miles`

`City = 130\ miles`

Explanation:

Given

`Highway = 31mi/gallon`

`City = 26mi/gallon`

`Total\ Miles = 285`

`Total\ Gallons = 10`

Required

Determine the number of miles driven on the highway and on the city

Represent the gallons used on highway with h and on city with c.

So, we have:

`c + h = 10` ---- gallons used

and

`31h + 26c = 285` --- distance travelled

In the first equation, make c the subject

`c = 10 - h`

Substitute 10 - h for c in the second equation

`31h + 26c = 285`

`31h + 26(10 - h) = 285`

Open bracket

`31h + 260 - 26h = 285`

Collect like terms

`31h - 26h = 285 - 260`

`5h = 25`

Make h the subject

`h = (25)/(5)`

`h = 5`

Substitute 5 for h in
`c = 10 - h`

`c = 10 - 5`

`c = 5`

If on the highway, he travels 31 miles per gallon, then his distance on the highway is:

`Highway = 31 * 5`

`Highway = 155\ miles`

If in the highway, he travels 26 miles per gallon, then his distance on the highway is:

`City = 26 * 5`

`City = 130\ miles`