A remote control car races straight down the street at 26 miles per hour. Two hours later, a second remote control car races straight down the same street at 52 miles per hour in pursuit of the first car. From the moment the first car started, how many hours will it take the second car to catch up to the first?
On what scale is the speed of each car measured?

Call the number of hours ’H’.

The second car will travel for ’H’ hours.
It will travel (52H) miles before it catches up.

The first car started out 2 hours earlier, so it travels for (H + 2) hours.
It will travel 26(H + 2) miles before the second car catches it.

Both cars start out from the same place.   (It’s not stated in the problem, but
that’s the problem’s fault.   If they don’t both start from the same place, then
there’s not information given to solve the problem. )

They start from the same place, and meet at the same place, so they both
travel the same.

52H = 26 (H + 2)

52H = 26H + 52

Subtract 26H from each side:

26H = 52

Divide each side by 26 :

H = 2.

The second car catches up to the first car 2 hours after the second car leaves.

The cars can be Nascars, Formula Whatevers, diesel pickups, or twisted wrecks.
The scale on which their speed is measured has no more effect on the answer than
the scale on which their weight is measured has.

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