As of 2018, taxi cab tariffs for working hours in London, England, are as follows. • For the first 234.8 metres or 50.4 seconds (whichever is reached first) there is a minimum charge of 2.60 GBP. • For each additional 117.4 metres or 25.2 seconds (whichever is reached first), or part thereof, if the distance travelled is less than 9656.1 metres there is a charge of 0.20 GBP. • Once the distance has reached 9656.1 metres then there is a charge of 0.20 GBP for each additional 86.9 metres or 18.7 seconds (whichever is reached first), or part thereof. (a) Develop a piecewise linear model for the cost, C, of a taxi ride based on the distance travelled, m, in metres. (b) Find the cost of 0.2 km, 5 km, and 15 km rides. (c) Develop a piecewise linear model for the cost, D, of a taxi ride based on the time taken, t, in seconds, ignoring distance. (d) Find the cost of 0.5 minute, 5 minute, and 15 minute rides. (e) Given that the actual taxi fare is always the greater of the two models, find: (i) the cost of a ride that takes 10 minutes to go 4 km (ii) the cost of a ride that takes 5 minutes to go 4 km.
As of 2018, taxi cab tariffs for working hours in London, England, are as follows.
• For the first 234.8 metres or 50.4 seconds (whichever is reached first) there is a minimum charge of 2.60 GBP.
• For each additional 117.4 metres or 25.2 seconds (whichever is
reached first), or part thereof, if the distance travelled is less than
9656.1 metres there is a charge of 0.20 GBP.
• Once the distance has reached 9656.1 metres then there is a charge of 0.20 GBP for each additional 86.9 metres or 18.7 seconds (whichever is reached first), or part thereof.
(a) Develop a piecewise linear model for the cost, C, of a taxi ride based on the distance travelled, m, in metres.
(b) Find the cost of 0.2 km, 5 km, and 15 km rides.
(c) Develop a piecewise linear model for the cost, D, of a taxi ride based on the time taken, t, in seconds, ignoring distance.
(d) Find the cost of 0.5 minute, 5 minute, and 15 minute rides.
(e) Given that the actual taxi fare is always the greater of the two
models, find:
(i) the cost of a ride that takes 10 minutes to go 4 km
(ii) the cost of a ride that takes 5 minutes to go 4 km.
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