The truck drove past the gas station at a speed of 54 km / h. 2 hours later, a passenger car drove past the same gas station

| February 24, 2021 | education

The truck drove past the gas station at a speed of 54 km / h. 2 hours later, a passenger car drove past the same gas station in the same direction at a speed of 72 km / h. How long will it take and at what distance from the gas station will a passenger car catch up with a truck if it was driving in a straight line at a constant speed?

Vg = 54 km / h = 15 m / s.

Vl = 72 km / h = 20 m / s.

t = 2 h = 7200 s.

td -?

Sl -?

At the moment a car passed by the gas station, the distance to the truck S1 was S1 = Vg * t.

Since the truck and the passenger car move in the same direction, the speed of the passenger car relative to the truck Vlg is Vlg = Vl – Vg.

td = S1 / Vlg = Vg * t / (Vl – Vg).

td = 15 m / s * 7200 s / (20 m / s – 15 m / s) = 21600 s = 6 h.

Sl = Vl * td.

Sl = 20 m / s * 21600 s = 432000 m = 432 km.

Answer: a passenger car will catch up with a truck in time td = 6 hours at a distance of Sl = 432 km from the filling station.



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