The important formula to this problem is \(distance=rate(time)\) or \(d=rt\)
Now, the speed of the car is 70 km/h, and the speed of the truck is 50 km/h. It will take the two vehicles the same amount of time to meet since they both left at the same time. So, since distance equals rate times time, and t = time:
the distance of the car = 70t
the distance of the truck = 50t
Because they both left in opposite directions, and the towns are 420 kilometers apart, the equation for this would be
\(70t+50t=420\)
We now solve the equation.
\(70t+50t=420 \\ 120t=420 \\ \frac{120t}{120}= \frac{420}{120} \\ t=3 \frac{1}{2}\)
It will take the vehicles 3 and a half hours to meet. Since we're looking for the time, 3 and a half hours from 10:00 AM is 1:30 PM.
So, the car and the truck will pass each other at 1:30 PM.
