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OSH2 solutions part 1
Differential Calculus With Applications To Life Sciences (MATH 102)
The University of British Columbia
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km
mins
Women’s VGH
St. Paul
1 2 3 4 5 6 7 8 9
6
12
18
24
30
36
42
48
At anyxvalue, we choose the hospital the shortest time away, sof 1 (x) looks like this:
km
mins
f 1 (x)
1 2 3 4 5 6 7 8 9
6
12
18
24
Bus
While riding on the bus, you travel only north, at a constant speed of onekilometre each minute. After you get offthe bus, you travel at 1 kilometre every 12 minutes. Since there are no bus stops labelled after Nelson,f 2 (x)doesn’texist whenx> 7 .5.
Whenx≤ 2 .5, the fastest route to a hospital is to disembark at King Edward and walk to the Women’s Hospital. The time this takes is the driving time plus the walking time. The walking time is fixed, but the driving time depends on x:(2. 5 −x)+(1. 5 ∗12) = 20. 5 −x.
Whenx≤ 4 .5, we have the option of disembarking at Broadway or at Nelson. From Broadway, the closest hospital is VGH, 2 km (30 min) away. However, if we stay on the bus from Broadwayuntil Nelson, we can get to St Paul’s in 3 + (18) = 21 minutes. So, disembarking at Broadway is never thefastest option. When 2. 5 <x≤ 7 .5, f 2 (x)=(7. 5 −x) + 18 = 25. 5 −x.
OSH2 solutions part 1
Course: Differential Calculus With Applications To Life Sciences (MATH 102)
University: The University of British Columbia
