Algebra 1-round trip

Question

Jed rode his scooter to school at 12 miles per hour and then jogged back at 6 miles per hour. If the round trip took him 6 hours, how far was it to school?

Answer 1

Distance = (Rate)(Time)

Let x = time jogging. Then 6 - x = time on scooter.

Distance to school = Distance from school

12(6 - x) = 6x

72 - 12x = 6x

18x = 72

x = 4 hours

Distance = (6 miles/hour)(4 hours) = 24 miles

Answer 2

Let x represent his time riding the scooter.

Let y represent the time he jogged.

Note that y = 6 - x.

Therefore,

12x = distance from home to school

6y = 6(6-x) = distance from school to home

12x = 6(6-x) = 36 -6x

Add 6x to both sides of this equation:

18x = 36

Divide both sides by the coefficient of x, 18 in this case:

x = 2 hours.

12 miles per hour times 2 hours = 24 miles to school.

Check:

6*(6-2) = 6*4 = 24 miles home from school.