Answer:
t = (tā Ā· vr)/ (vj - vr) = 45 seconds
Step-by-step explanation:
Given:
Initial time from Ricardo Ā tā = 15 seconds, Ricardo's velocity (speed) vr = 3 ft/s,
John's velocity (speed) vj = 4 ft/s
Requested time when John catch Ricardo t = ?
During 15 seconds, Ricardo moved away
S = vr Ā· tā = 3 ft/s Ā· 15 s = 45 feet.
From that moment, the same time runs for both of them
Ricardo's path is Sā = vr Ā· t Ā and John's path is Sā = vj Ā· t
S + Sā = Sā => Ā S = Sā - Sā Ā => 45 = vj Ā· t - vr Ā· t Ā
When we draw t we get:
t ( vj - vr) = 45 Ā t = 45 / (vj - vr) = 45 / (4 - 3) = 45 / 1 = 45 seconds
t = 45 seconds
Sā = vr Ā· t = 3 Ā· 45 = 135 ft
Sā = vj Ā· t = 4 Ā· 45 = 180 ft
