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Traffic Tunnel

Age 14 to 16 Short Challenge Level:

Answer: None of the vehicles will fit through the tunnel.


  a) truck                                        b) coach                                      c) lorry

             


How high is the tunnel at $x=1, x=1.5, x=2$?

  $x=1\Rightarrow y=\frac49(9-1)=\frac{32}9=3\frac59=3.\dot5$

$x=1.5\Rightarrow y=\frac49(9-1.5^2)= \frac49\left(\frac{36}4-\frac94\right) = 4-1=3$

$x=2\Rightarrow y=\frac49(9-2^2)=\frac49\times5=2\frac29=2.\dot2$



All of the vehicles are too tall (or too wide) for the tunnel:
 
$3.9\gt3.\dot5$

$3.4\gt3$

$2.7\gt2.\dot2$




 
You can find more short problems, arranged by curriculum topic, in our short problems collection.