Can You Count Cars?

Algebra Level 4

Car A traveled Southward for 120 km. at 100 km/hr. During this trip it met 78 vehicles going Northward.

What is the rate of vehicular traffic Northward?( in vehicles/hr).

Assume that the northbound traffic was also going 100 km/hr.


The answer is 32.5.

Guiseppi Butel by Guiseppi Butel , 90, Canada

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2 solutions

Bob Kadylo
Apr 16, 2016

If you think of the approaching Northbound cars as wavefronts of sound, then this problem is related to the Doppler Effect in Physics. f s o u r c e = V N ∗ f o b s e r v e d V N + V S \displaystyle f_{source} = \frac {V_N*f_{observed}}{V_N+V_S} where V=velocity, N=north, S=south, f=frequency. The observed frequency is 78 vehicles in 1.2 hours = 65 vehicles per hour. The source frequency (Northbound cars per hour) is, therefore: f s o u r c e = 100 ∗ 65 100 + 100 = 32.5 f_{source}= \frac {100*65}{100+100} =32.5

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Moderator note:

Nice relation to a physics concept!

Of course, the proof of the formula can be mathematically derived :)

Guiseppi Butel
May 16, 2014

In 1 hour Car A met 100/120 X 78 = 65 vehicles. The # of vehicles passing a fixed point in that hour is 1/2 of this which is 32.5

1 Helpful 0 Interesting 0 Brilliant 0 Confused

sir can you please elaborate your solution?

Jun Arro Estrella - 5 years, 5 months ago

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