grace starts jogging home at 5 kmhr will leaves 10 minutes l

grace starts jogging home at 5 km/hr. will leaves 10 minutes later on a bike (from the same place) riding at 15 km/hr. how long will it take will to catch up to grace?

Solution

Grace DATA:
rate = 5 km/h ; time = x hrs ; distance = rt = 5x km
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Will DATA:
rate = 15 km/h ; time = (x-(1/6)) hrs ; distance = rt = 15(x-(1/6)) km
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Equation:
distance = distance
5x = 15(x - (1/6))
5x = 15x - (5/2)
10x = (5/2)
x = 1/4 hr
x - (1/6) = (1/4)-(1/6) = (6-4)/24 = 2/24 = 1/12 hr. or 6 minutes