The distance from Ari’s house, A, to Ben’s house, B, is equal to the distance from Ari’s house to Cal’s house, C. One day the boys all met at Ari’s house, and then they went to Ben’s house, and from there to Cal’s house. Then Ari and Ben went home. Ari and Cal each wrote expressions for the distance they walked:
Ari’s travel distance: (2 + 1) + ( − 4) + (2 + 1)
Cal’s travel distance: 2(2 + 1) + ( − 4)
Did Ari and Cal walk the same distance? Explain.
In the expression for Cal’s distance, why do you think (2 + 1) is multiplied by two?
Did Ben walk the same distance as the other two boys? Explain. Write an expression to represent the distance Ben walked.