Question

If 3 cars have traveled a total of 180,000 miles and the distance traveled by each car differs by at least 1 mile from the distance traveled by either of the other 2 cars,what is the minimum possible number of miles traveled by the car with the most mileage

Answer 1

60001 miles

Explanation:

Given

`Total\ Distance = 180000`

Let the cars be:
`Car\ A, Car\ B\ and\ Car\ C`

Assume that Car A has the minimum mileage of x.

`Car\ A = x`

The other cars would be:

`Car\ B = x + 1`

`Car\ C = x + 2`

This implies that Car C has the highest mileage

Required

Determine the possible minimum number of miles

Since the total distance is 180000, then:

`Car\ A + Car\ B + Car\ C = 180000`

Substitute values for Car A, B and C

`x + x + 1 + x + 2 = 180000`

Collect Like Terms

`x + x + x = 180000-1-2`

`3x = 179997`

Divide both sides by 3

`(3x)/(3) = (179997)/(3)`

`x = (179997)/(3)`

`x = 59999`

The car with the most mileage is Car C

So:

`Car\ C = x + 2`

Substitute 59999 for x in
`Car\ C = x + 2`

`Car\ C = 59999 + 2`

`Car\ C = 60001`

The minimum distance travelled by Car C is 60001 miles