Re: Two trucks travel from Alphaburg to Betaville along the same route.

Two trucks travel from Alphaburg to Betaville along the same route. The speed limit for the first 30 miles is 60 miles per hour. The speed limit for the next 10 miles is 40 miles per hour, and the limit for the final 60 miles is 55 miles per hour. Truck F has a maximum speed of 70 miles per hour, but Truck S has a speed-limiting governor installed to cap its maximum speed at 50 miles per hour. Truck S departs Alphaburg 12 minutes before Truck F.

If each truck travels at the lesser of the speed limit or the maximum speed of the truck, how far from Betaville is the point where Truck F catches up with Truck S?

Let's assume that Truck S depart at 00:00 hrs and Truck F departs at 00:12 hrs

First 30 miles (max speed limit = 60 miles per hour) : -
Truck S cross in 30/50 = .6 hrs = 36 minutes
Truck F cross in 30/60 = .5 hrs = 30 minutes
Truck F gains 6 minutes w.r.t. Truck S
Time left to make up = 12 - 6 = 6 minutes = .1 hours

Next 10 miles (max speed limit = 40 miles per hour) : -
Truck S cross in 10/40 = .25 hrs = 15 minutes
Truck F cross in 10/40 = .25 hrs = 15 minutes
Truck F gains 0 minutes w.r.t. Truck S

Final x miles (max speed limit = 55 miles per hour) : -
Truck S cross in x/50 hrs
Truck F cross in x/55 hrs
Truck F gains (x/50 - x/55 = x/550) hrs w.r.t. Truck S
x/550 = .1
x = 55 miles

The point where Truck F catches up with Truck S = 30+10+55 = 95 miles away from Alphaburg
The point where Truck F catches up with Truck S = 30+10+60 - 95 = 5 miles away from Betaville

IMO A