by Mikayla
(Oklahoma, United States)
A truck left a depot at noon traveling an average speed of 40 kilometers per hour. How far from the depot and what time will it overtake another truck, which left the same depot 2 hours earlier and was traveling 30 kilometers per hour.
Let t be the time it takes the truck traveling 40 km/h to overtake the truck traveling 30 km/h.
Then, the truck traveling 30 km/h will be overtaken in t + 2 hours
Truck traveling 40 km/h
d = vt
d = 40t
Truck traveling 30 km/h
d = vt
d = 30(t+2)
Truck traveling 40 km/h will meet with truck traveling 30 km/h when the distance is the same.
40t = 30(t + 2)
40t = 30t + 60
40t - 30t = 30t - 30t + 60
10t = 60
Since 10 times 6 = 60, then t = 6
Truck traveling 40 km/h will overtake the other truck after 6 hours or at 6:00 pm
d = 40 x 6 = 240
d = 30 x(6 + 2)
d = 30 x 8 = 240
The trucks will be 240 km away from the depot.
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