# Rebuilt

Steve owns an antique car, which is on its second engine. The combined age of the car and the engine is 84 years. The car is currently twice as old as the engine was when the car was as old as the engine is now. How old are they now?

### 2 guesses to Rebuilt

• Tiffy

The car is 48 years old and the engine is 36 years old now.

Solution:

Let C = the age of the car now.
Let E = the age of the engine now.

The car is currently twice as old as the engine was “when the car was as old as the engine is now”.

E is the age of engine now. When the car was E years old like the age of engine now, that was C – E years ago.

Therefore: (C – E) years ago = when the car was as old as the engine is now

The car is currently twice as old as ” ‘the engine was’ when the car was as old as the engine is now”.

C – E years ago, what was the age of the engine? E – (C – E), which gives
you 2E – C.

Therefore: 2E – C = the engine’s age when the car was as old as the engine is now.

The car is currently twice as old as the engine was when the car was as old as the engine is now.

The car now, C is twice as old as 2E – C, so C = 2(2E-C)

Solving this, we get 3C = 4E

C + E = 84 because the sum of their ages now is 84, then we solve the two equations:

C + E = 84
C = 84 – E
3(84-E) = 4E
252 – 3E = 4E
252 = 7E
E = 36
Since C + E = 84,
C = 48

Thus, the car is 48 years old and the engine is 36 years old :)

• Dude

You’re right, Tiffy!

Couldn’t have explained it better myself.

You’re today’s winner.