Maths tasks. Travelling to partner countries

1. Vilnius to Athens by Car
We are planning to travel from Vilnius (Lithuania) to Athens (Greece) by car. There are several routes that we can
choose. Let’s consider two of them. One will go through:
1. Vilnius-Warsaw-Brno-Bratislava-Budapest-Belgrade-Athens

2. The second will go through
2. Vilnius-Brest-Lviv-Timisoara- Belgrade-Athens
As we see, the difference between these routes is in the Vilnius to Belgrade part. The route #1 goes through the
Central Europe. The route #2 traverses Eastern Europe. Because economies of the Central European countries are
tightly integrated, we can say that the gasoline price is approximately the same in all the countries that we pass. Let’s
say it is 1.1 EUR per liter. The distance from Vilnius to Belgrade by route #1 is 1700 km and estimated driving time is
19 hours.
Gasoline prices are different in Eastern Europe. The table below gives gasoline price per liter in local currency, the
exchange rate to euro and the distance to be travelled in a particular country.
Country Gasoline price
(per liter)
Currency Exchange rate
(for 1 EUR)
Distance to
travel (km)
Time to
travel
(hours)
Belarus 1.2 BYR (Belarusian Ruble) 2 360 5
Ukraine 24.5 UAH (Hryvna) 28.7 670 13
Romania 4.9 RON (Leo) 4.52 470 7
A. Using this table and an assumption that the fuel consumption of our car is 40 liters for 6 hours of driving,
recommend which route should we choose.

3. The distance from Belgrade to Athens is 1100 km with the estimated driving time 12 hours. The average gasoline
price on this part of the trip will be 1.35 EUR/liter.
B. Assuming the price for a flight ticket from Vilnius to Athens is 300 EUR, what transport would you choose for 2
travelers – car or plane? Note: if travelling by car, we will have to spend 200 EUR for two nights stay and food.
Solution
A.
1. We are spending 40l/6h = 6.67 liters per hour.
2. Per 19 hours of driving via Route #1 we will spend: 19 h * 6.67 l/h = 127 l.
3. This will cost us 127 l * 1.1 EUR/l = 139.7 EUR.
4. According to the driving times, we will spend:
6.67 l/h * 5 h = 33 l – in Belarus;
6.67 l/h * 13 h = 87 l – in Ukraine;
6.67 l/h * 7 h = 47 l – in Romania.
5. The fuel cost in EUR in these countries is:
1.2 (BYR/l)/2 (BYR/EUR) = 0.6 EUR/l – in Belarus;
24.5 (UAH/l)/28.7 (UAH/EUR) = 0.85 EUR/l – in Ukraine;
4.9 (RON/l)/4.52 (RON/EUR) = 1.08 EUR/l – in Romania.
6. The total fuel cost on Route 2 to Belgrade is:
33* 0.6 + 87 * 0.85 + 47 * 1.08 = 144.5 EUR
Answer A: Driving via Route #1 is cheaper.
B. On the way from Belgrade to Athens we will burn 6.67 l/h* 12 h = 80 l of gasoline. This will cost us 80 l * 1.35
EUR/l = 108 EUR. Thus, we need to put aside ~250 EUR for gasoline. Adding food and lodging, the car trip
from Vilnius to Athens will cost us ~450 EUR.
Answer B: Driving from Vilnius to Athens is less expensive than a flight, if there are more than one person in
the car.

4. Vilnius to Larnaca by Air
In preparation for a trip from Vilnius (Lithuania) to Nicosia (Cyprus), we searched for a flight from Vilnius to Larnaca.
Two options attracted our attention (airport codes are provided in parentheses):
1. Vilnius (VNO) – Moscow (SVO) – Larnaca (LCA) by Aeroflot
2. Vilnius (VNO) – Frankfurt (FRA) – Athens (ATH) – Larnaca (LCA) by Lufthansa

5. The price of Aeroflot ticket is $335. The price offered by Lufthansa is $580. One can assume that the second flight is
more expensive, because it is longer and requires more fuel.
The table below lists the length of all legs in kilometers and the estimated flight time. Both carriers are flying Airbus
320-200 on these routes, which fuel consumption is 77 miles per gallon per seat.
Flight Leg Distance (km) Flight Time
VNO-SVO 780 1h 25m
SVO-LCA 2365 3h 50m
VNO-FRA 1245 2h 10m
FRA-ATH 1820 2h 45m
ATH-LCA 930 1h 35m

6. A. Taking the reference price for the Jet fuel as $1.6 per gallon, calculate what portion of the price difference is
attributed to the fuel cost.
B. During the first 5 minutes of takeoff airplanes burn 4 times more fuel than in the cruising regime. Estimate how
much should be added to the fuel cost per seat due to the additional leg in the Lufthansa route.
Solution
A.
a. The total length of Route 1 is: 780 km + 2365 km = 3145 km.
b. The total length of Route 2 is: 1245 km + 1820 km + 930 km = 3995 km.
c. The length difference between two routes is: 3995 km – 3145 km = 850 km.
d. Since fuel consumption is given to us in miles per gallon, we need to convert kilometers to miles: 850
km = 850/1.6 miles = 531 miles.
e. Fuel consumption per seat for 531 miles is: 531 miles/77 miles/gallon = 6.9 gallons.
f. The cost of 6.9 gallons is: 6.9 gallons * 1.6 $/gallon = 11.04 $.
Answer A: The fuel cost difference per seat between two routes is about $11.
B.
a. Let’s take the first leg VNO-SVO as an example. 5 minutes of takeoff constitute:
5/85 = 6% of the flight time. During this flight period, we have additional 300% of fuel consumption.
Thus, we need to add 6% * 300% = 18% to the fuel cost of the entire flight. Per section A, the fuel
cost for 780 km flight is:
780 (km)/1.6 (km/mile)/77 (mile/gallon) * 1.6 ($/gallon) = 10 ($).
18% of $10 is $1.8.
Answer B: Fuel cost of the additional takeoff is $1.8 per seat.

7. Vilnius to Taranto
1. The distance from Vilnius (Lithuania) to Taranto (Italy) is 2635.2 kilometers by car, while the straight distance is
1,680.1 km.
Round off this number to tens and calculate the absolute and rounding relative (percentage to three decimal places)
errors.
2. Traveling from Vilnius to Taranto city by plane is Vilnius – Milan – Brindisi, after the flight continue travelling by
train. The table shows the flight time.
Departures from Arrives in
Vilnius (VNO) 18:10 Milan (BGY) 19:45
Milan (BGY) 21:35 Brindisi (BDS) 23:15
Find out what is the time difference between Lithuania and Italy and calculate the flight duration from Vilnius to
Brindisi.
Solution
1. 2635,2 ≈ 2640, 1680,1 ≈ 1680.
The absolute error: |2635,2 − 2640| = 4,8 , |1680,1 − 1680| = 0,1 .
Relative error:
4,8
2635,2
∙ 100 % ≈ 0,182,
0,1
1680,1
∙ 100% ≈ 0,006
2. Time difference 1 hour. 2 h 35 min + 2 h 40 min = 5 h 15 min.

8. Vilnius to Überlingen
When travelling from Vilnius (Lithuania) to Überlingen (Germany) firstly, you fly by plane to Stuttgart and continue
the journey by car. The distance between Stuttgart and Überlingen is 174 kilometers, you need about 1 hour 45
minutes to travel it. There is also a planned 20 minute stop.
1. How long will it take to travel from Stuttgart to Überlingen? Write the answer in hours as a fraction.
2. Calculate
a. The averge driving speed (km/h integer);
b. The average journey speed (km/h).
3. During 100 kilometers a car consumes an average of 7 liters of petrol. The price for 1 liter of petrol is 1,32 €. How
many euros will the fuel cost?
Solution
1. 2 ℎ 5 𝑚𝑖𝑛 = 2
1
12
ℎ.
2. a.
174 𝑘𝑚
1,75 ℎ
≈ 99 𝑘𝑚/ℎ; b.
174 𝑘𝑚
25
12
ℎ
= 83,25 𝑘𝑚/ℎ.
3. € 16,08

9. Vilnius – Czestochowa
Distance between Vilnius and Czestochowa — 674 km.
Average travel time: Vilnius — Czestochowa: 12 h 45 min.
Time zone difference between Vilnius and Czestochowa - 1 hour.
Tasks:
1. What is the average speed of the bus, if the distance of 674 km it overcomes roughly in 12 hours and 45 minutes.
Round off the answer to the nearest whole number.
2. What is the fare in zloty (PLN)? Changing the fare into zloty, please refer to the date of the exchange rate.
3. What time does the Lithuanian-time bus will arrive in Czestochowa?
4. How long would the journey take, if the bus on the road repair of 106 kilometers would go twice slower than the
average, while the rest of the way at normal speed? At what time (local time) the bus would arrive at
Czestochowa? Round off the received answers to the nearest whole number.
5. What is the distance between Vilnius and Czestochowa in miles, if 1 mile = 1,609344 km. Give the answer in 0,001
mile accuracy.
Solution
1. 53 km/h
2. About 134,02 PLN
3. 11 h
4. 14 h; 11:15.
5. 418,804 mi

10. Vilnius - Konya
Cheapest flight:
Fastest flight:
Tasks:
1. What average speed is needed to drive 3375 km distance within 41 h 24 min? Submit the answer with accuracy of
0.01 km/h.
2. How many times the fastest flight is more expensive than the cheapest flight? Round off the answer to one
decimal.
3. How many times the cheapest flight is longer than the fastest flight? Round the answer off pieces
4. How much does the cheapest flight cost in Turkish Lira? Please refer to the date of exchange rates while changing
currency.
5. When in Lithuanian time zone will we reach Konya, if we choose the fastest flight?
Solution
1. 81.52 km/h;
2. 10.3 times
3. 3 times
4. Around 1069.96 TRY;
5. 1 h 55 min.