Reddit has a lot of great puzzles, like this one: MATH PROBLEM

Vehicles are traveling on the same route. First they pass point A, then point B. Vehicles pass point A in equal time steps in the following order: a bus, a motorcycle, and a car. They pass by point B at the same time intervals again transportation: bus, car and motorcycle. Find the speed of the bus if the speed of the car is 90 km/h and the speed of the motorcycle is 60 km/h.

Read more: The velocity of vehicles

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So here’s the situation, for B(us), M(otorcycle) and C(ar).

At t0 + 0δ B passes point A.

At t0 + 1δ M passes point A.

At t0 + 2δ C passes point A.

At t1 + 0δ B passes point B.

At t1 + 1δ C passes point B.

At t1 + 2δ M passes point B.

Whatever the distance is between the 2 points, this is how long the vehicles spend crossing.

C: t1 – t0 – δ

M: t1 – t0 + δ

B: t1 – t0

We know that v * t = d, velocity * time = distance. This gives us 3 new equations. For now, I’m not using any units, and t = t₁ – t₀, and we’re looking for v_b.

90 * (t – δ) = d

60 * (t + δ) = d

vb * t = d

In all 3 equations d is the same. Therefore:

90 * (t – δ) = 60 * (t + δ) <=>

90t – 90δ = 60t + 60δ <=>

30t = 150δ <=>

δ = t/5

Returning to the bus, we have:

v_b * t = d <=>

v_b = d/t <=>

v_b = 90 * (t – δ) / t <=>

v_b = (90t – 90δ) / t <=>

v_b = (90t – 90 * t/5) / t <=>

v_b = (90t – 18t) / t <=>

v_b = 90 – 18 <=>

v_b = 72

Adding back the units, the answer is 72 km/h.