Speed word problem

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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