How many miles from the starting point will the two vehicles draw level?

Question

Two vehicles set off from the same point to travel the same journey.

The first vehicle sets off three minutes before the second vehicle.

If the first vehicle travels at 40 mph and the second vehicle travels at 70 mph, how many miles from the starting point will the two vehicles draw level?

Answer 1

Distance traveled by the first vehicle in the initial 3 minutes = 40*3/60 = 40/20 = 2 miles
Now the speed of the second vehicle with respect to the first one = 70 - 40 = 30 mph
The gap of 2 miles between the vehicles will move with the 2 vehicles and also become smaller over time because of the higher speed of the second vehicle.
now time taken by the second vehicle to close the 2 mile gap = 2/(30) = (1/15) hr = 4 minutes.
Distance traveled by the second vehicle in 4 minutes = 70*(1/15) = 4 + (2/3) miles = 14/3 miles
It can also be calculated by taking the first vehicle's perspective: (2 miles) + (40*(4/60)) = 2 + (2/3)*4 = 2 + 8/3 = 14/3 miles.