The front wheels of a vehicle are 15 cm greater in circumference than the back wheels. THe back wheels make 3 revolutions more than the front wheels in a distance of 15 m. Find the circumference of the front wheels.

1. The front wheels of a vehicle are 15 cm greater in circumference than the back wheels.
2. The back wheels make 3 revolutions more than the front wheels in a distance of 15 m.


Distance traveled = revolutions x circumference
Revolutions = R, Circumference = C

1. Circumference relation: C(f) = C(r) + 15 cm

The distance traveled by the front wheel is 15/C(f). It is equal to the distance traveled by the rear wheel, 15/C(r). The number of revolutions traveled is

2. Revolutions relation: 15/C(f) = 15/C(r) - 3

This gives you two equations and two unknowns. If you wish, you can use different variables than I have, to try to make it clearer

F = circumference of front wheel
R = circumference of rear wheel

F = R + 15

\frac {15}{F} = \frac {15}{R} - 3

Can you solve it now?

Ok, to start, assign variables to the circumference of the wheels.

Let f be the circumference of the front wheel
Let b be the circumference of the back wheel.

1. f - 15 = b
(For them to be equal, you have to remove 15 cm from the circumference of the front wheel)

2. In 15 m, the back does 3 more revolutions. Revolutions are given by the distance covered divided by the circumference of the wheel.
So,
The revolutions by the back wheel are given by \frac{1500}{b}
That of the front wheel are given by \frac{1500}{f}

Since the back wheel does 3 more revolutions, for them to be equal, you have to remove 3 from the number of revolutions of the back wheel:

\frac{1500}{b}-3 = \frac{1500}{f}

Now, you have your two equations to solve.

I suggest using substitution here, substituting b in the second equation by (f - 15). Eventually, you'll obtain the answer for f, the circumference of the front wheels.

If you have any difficulty, feel free to ask! :)