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

Answer:

60001 miles

Step-by-step 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

$\frac{3x}{3} = \frac{179997}{3}$

$x = \frac{179997}{3}$

$x = 59999$

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