Question

Please help NEEDED ASAP!!!!

taxi cab tariffs 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), 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)
1. Develop a piecewise linear model for the cost, C, of a taxi ride based on the distance travelled, m, in metres.
2. Find the cost of 0.2 km, 5 km, and 15 km rides.
3. Develop a piecewise linear model for the cost, D, of a taxi ride based on the time taken, t, in seconds, ignoring distance.
4. Find the cost of 0.5 minute, 5 minute, and 15 minute rides.
5. 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 (if) the cost of a ride that takes 5 minutes to go 4 km

Answer 1

1. A piecewise linear model for the cost, C, of a taxi ride based on the distance travelled, m, in meters can be represented as:

C = 2.60 (m<234.8)

C = 2.60 + 0.20(m-234.8) (234.8<=m<9656.1)

C = 2.60 + 0.20(9656.1-234.8) + 0.20(m-9656.1) (m>=9656.1)

2.To find the cost of 0.2 km, 5 km, and 15 km rides:

0.2 km = 200 m, the cost would be 2.60 GBP

5 km = 5000 m, the cost would be 2.60 + (0.20 * (5000-234.8)) GBP = 2.60 + 858 GBP = 1118 GBP

15 km = 15,000 m, the cost would be 2.60 + (0.20 * (9656.1-234.8)) + 0.20(15,000-9656.1) GBP = 2.60 + (0.20 * 9656.1-234.8) + 0.20(15,000-9656.1) = 2.60 + 1712.2 + 2040 = 3964.8 GBP

3. A piecewise linear model for the cost, D, of a taxi ride based on the time taken, t, in seconds, ignoring distance can be represented as:

D = 2.60 (t<50.4)

D = 2.60 + 0.20(t-50.4) (50.4<=t<1260)

D = 2.60 + 0.20(1260-50.4) + 0.20(t-1260) (t>=1260)

4. To find the cost of 0.5 minute, 5 minute, and 15 minute rides:

0.5 minute = 30 seconds, the cost would be 2.60 GBP

5 minutes = 300 seconds, the cost would be 2.60 + (0.20 * (300-50.4)) GBP = 2.60 + 44 GBP = 2.60+44 = 3.04 GBP

15 minutes = 900 seconds, the cost would be 2.60 + (0.20 * (1260-50.4)) + 0.20(900-1260) GBP = 2.60 + (0.20 * 1260-50.4) + 0.20(900-1260) = 2.60 + 252 + -12 GBP = 2.48 GBP

5. 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 is 1118 GBP (by distance model)

(ii) the cost of a ride that takes 5 minutes to go 4 km is 3.04 GBP (by time model)

It is important to