Math Trail

Math Trail

Lions' Gate Bridge Math Problem Solutions

Lions' Gate Bridge Solutions

1. Solution

4 km = 4000 m

4000 – 1823 = 2177

Length of the Stanley Park Causeway is 2177 m.

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2. Solution

187.28 + 472.75 + 187.28 = 847.31

1823 – 847.31 = 975.69

Length of north viaduct is 975.69 m.

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3. Solution

472.75: 2 = 236.375

y=ax²

55 = a (236.375 )²

a = 9.84 ×10^-4

236.375 –40 = 196.375

Y = 9.84 ×10^-4( 196.375)²

Y = 37.946 m

Height of cable above the road at that point is: 37.946 + 5 = 42.946 m.

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4. Solution

80× 800 = 64000

80× 2 = 160

160 + 50 =210

210 ×80 = 16800 kg

10( 80 + 20 ) = 1000 kg

64000 + 1000 + 16800 = 81800 kg

Active load on the bridge is 81800 kg.

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5. Solution

a) V = x = 4 = 0.08h

t 50

It takes takes 4 minutes and 48 seconds to pass over the bridge if a car is travelling an average speed of 50 km/hr the average speed.

b) If the average speed is reduced by half to 25 km/hr then the time to cross the bridge will double to approximately 9 minutes and 36 seconds.

You may also calculate this answer as in part a):

V = x = 4 = 0.16h

t 25

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6. Solution

65000 ×2 = 130000 number of people per day

130000 ×365 = 47450000 number of people per year

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7. Solution

99.9 + 8.2 + 16.9 = 125

The total budget for replacement and rehabilitation of the bridge is $125 million.

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8. Solution

V = x

t = x = 1.823 = 0.03h

V 60

It takes just one minute and forty-eight seconds.

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9. Solution

Let x = the number of total trips via Lions Gate and Second Narrow Bridge

Average of 60000and 70000 = 13000/2 = 65000

40% x = 65000

40x = 65000

100

x = 16250

Total trips across Burrard Inlet are 16250.

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10. Solution

5000× 365 = 2,372,500

On annual basis, about 2,372,500 vehicles pass over the Lions Gate Bridge.

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11. Solution

y=ax²

196.375 = a ( 37.946)²

a = 9.84 *10^-4

236.375 –40 = 196.375

Y = 9.84 *10^-4x²

Axis of symmetry is x=0 and y-intercept is ( 0, 0 ).

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12. Solution

3000 + 2250 = 5,250

Average number of vehicles during rush hours is 5,250.

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13. Solution

3 × 3.5 + 2 ×2.67 + 2 = 17.84 m

The total length of the Lions Gate Bridge after replacement is 17.84 m.

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14. Solution

2003 – 1937 = 66

Lions Gate Bridge is 66 years old.

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15. Solution

Average number of vehicles pass over the bridge is 65000 per day.

65000 ×365 × 5 = 118,625,000

$118,625,000 would be collected after five years.

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