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.

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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.

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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





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.
(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
That of the front wheel are given by

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:



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! :)