Math Trail

SOLUTIONS:

Environmental Math Problems



Back to Environmental Transportation


TYPES OF TRANSPORTATION:

1)  Average number of trips per person = 5.5 ¸ 2 = 2.75 trips per person

2)  

Type of Transport Trips per Transportation Mode
Automobile Automobile Trips:  5.5 x 74% = 4.07 million trips
Bike Bike Trips:  5.5 x 14% = 0.77 million trips
Walking Walking Trips:  5.5 x 10.3 % = 0.57 million trips

3)  Circle Graph that represents this information:

Top

COSTS:

4)  Monthly Average Cost = $220 ¸ 12 = $18.3 dollars per month

5a) The concession fare is 63.5% of the regular adult fare. (Calculation: 40 ¸ 63 = 63.5%)

5b) [Answers will vary.]

6)  The student ratio (75%) is bigger than the adult ratio (66.7%) by 8.3%

Calculation
Ratio - 1 zone : 2 zone
Adult - 2 : 3 (66.7%)
Concession - 1.5 : 2 = 3 : 4 (75%)

7)  To make it financially worth it to get a transit pass:

8)  Monthly savings by a student who buys a pass:  Assuming 4 weeks of 5 school days gives us 20 days in a month.  Each day the student would spend $3 on transit tickets, thus in a month the student would spend 20 x $3 = $60.  Since the monthly pass is $40, the student would save $20. 

Top
Annual Cost for 2002 Chevrolet Cavalier 4 Cylinder
km / Year `` Variable Costs   Fixed Costs Total Costs Cost / km 
12,000 km/year $1,470.00``` $6263.40    
18,000 km/year $2,205.00 $6,263.40    
32,000 km/year $3,920.00 $8,027.40    

Computed Table for Questions 9 & 10

Annual Cost for 2002 Chevrolet Cavalier 4 Cylinder
km / Year `` Variable Costs   Fixed Costs Total Costs Cost / km 
12,000 km/year $1,470.00``` $6263.40 $ 7733.40 64¢
18,000 km/year $2,205.00 $6,263.40 $ 8468.40 47¢
32,000 km/year $3,920.00 $8,027.40 $11947.40 37¢

10)  The distance that gives you the cheapest cost per km is the greatest distance travelled per year - 32,000 km/year.

11)  Percentage of total cost for each distance travelled:

12)  [Answers may vary.]

13)  [Answers may vary.] Possible Solution:

Type of Transport Cost per year
Car - driving 2002 Chevy Cavalier 32,000 km/yr $11947.40 (see chart above)
Bike $220 (given in Q4)
Public Transport - adult who buys passes monthly 12 * $63.00 = $756

Therefore:

14a) The family spends $723 on automobile expenses.

Calculation: 19.5% of the total cost is $385.  Then total budget = 385 ¸0.195 = $2026.  Automobile costs are 35.7 % of the total, so automobile costs are $723.

14b)  Their total monthly budget = $385 ¸0.195 = $2026

14c)  The parents spend $39.30 on clothing.

Calculation: The total clothing costs are 9.7% of $2026 = $196.5.  Of this, the parents spend 20%, which is $39.30 per month.

Top

15a)  Minimum number of participants = 130 cars x 4 passengers = 520 passengers

15b)  Maximum number of participants = 130 vans x 7 passengers = 910 passengers

15c)  If there are equal numbers of cars and vans, then there would be 65 x 4 + 65 x 7 = 715 passengers total

16)   There must be approximately 13 cars and 117 vans. 

Calculation:
Let x = number of cars.
Then 130 – x = number of vans
870 = 4x – 7(130-x)
870 = 4x + 910 – 7x
x = 13.3 
Thus there must be approximately 13 cars and 117 vans.
 

17) [Answers may vary.] Possible Solution: The ride-share trips account for approximately less than 1/10 of 1% of all automobile rides taken on any given day.  

Calculation:
74% of the 5.5 million trips made occur in automobiles - approximately  4,070,000 trips
Suppose that each ride-share vehicle makes 5 trips per day. Therefore a total of (130*5)=650
(650/4070000)*100 = (1.56 x 10-4)*100 = 1.56 x 10-2 = 0.0156 % 

18)  [Answers may vary.] 

Top

POLLUTION:

19) Given that all the lines between the years are straight, we can calculate the average by simply estimating the value at each year, and finding the average of these values (we do not need to calculate the area of the pollution using more complex methods).

Thus, estimating the values off the graph, the average pollution for ozone from 1994 to 2000 is:

            38 + 39 + 44 + 35 + 42 + 43 + 37 = 278¸7 = 39.7 % of the time

Similarly, for PM 10 the average pollution is:

            7.5 + 6.3 + 3.8 + 6.5 + 2.8 +3.0 = 26.1 ¸ 6 = 4.4 % of the time

20)  A likely reason for the sharp increase in 1998 was the huge number of forest fires that blazed throughout BC that summer.

21)  Light duty vehicles account for 58% of 357 000 tonnes.  Thus the answer is 207 060 tonnes.

22)  If light duty vehicles only produced half of their emissions, that would be 103 530 tonnes.  Then, total tonnage of emissions would be 357 000 – 103530 = 253 470 tonnes.  The percentage of emissions produced by light duty vehicles  is 103 530 ¸ 253 470 = 40.85 %

A circle graph representing this new distribution of pollutants is as follows:

23)  The CO emissions are 60 % of 357 000 tonnes, which is 214 200 tonnes.  Light duty vehicles produce 94% of CO, which is 201 348 tonnes of CO.

Top

Health Effects:

24)  The fact that there is an order of magnitude between the lower and upper limits in the number of deaths certainly points to ambiguity in the measuring of causes of death.  However, given that the lower limit is a small integer (15), this type of variation is not surprising, and much less significant than if the limits were bigger (for example in the thousands and tens of thousands).