Aford truck enters a highway and travels at a uniform speed of 50 mph. half an hour later a jaguar enters the highway at the same junction and heads in the same direction at 55 mph. how long after the ford entered the highway does the jaguar catch up with the truck?

Let the Jaguar travel for x hours to catch the truck.
Because the Jaguar begins to chase the truck after a half hour, the truck traveled for (x + 0.5) hours.

The distance the Jaguar traveled is
d₁ = (55 mph)*(x h) = 55x mi.

The distance the truck traveled is
d₂ = (50 mph)*(x + 0.5) = 50x + 25 mi

The two distances are equal, therefore
55x = 50x + 25
5x = 25
x = 5 hours

The Ford truck traveled for x+0.5 = 5.5 hours.

5.5 hours