**UCAT** **Question Analysis - Quantitative Reasoning Question 33**

A courier needs to drive from London to Paris and back to deliver a pack-ago. The following diagram sets out the route, together with the availability of petrol stations, Including prices and distances between each.

Between Calais and Dover, the car is loaded onto a ferry boat. The cost of a single ferry journey is £75. Including loading and offloading time, the ferry Journey takes 2 hours each way.

Exchange rate: £1.00 = E1.20. Capacity of the car's fuel tank: 45 litres. The car runs on unleaded petrol. 1 litre of petrol enables the car to drive for 10 km.

**If the courier drives at an average speed of 110 km/h between Lon-don and Dover and at an average speed of 120 km/h between Cal-ais and Paris, **

**Q33.1 how long will it take him to travel from London to Paris. assuming that he does not stop at any petrol station? **

a.3h 41 min

b.3h 49min

c.4h 41 min

d.5h 41min

e.5h 49min

**The driver sets out from London with a full tank of fuel. He heads towards Paris with the intention of turning back as soon as he has delivered the package. He forgets to check his fuel gauge and runs out of petrol. **

**Q33.2 At what distance from Paris will he stop?**

a. 10 km

b. 20 km

c. 30 km

d. 50 km

e. 70 km

**The courier sets out from London with 20 litres of fuel in his tank. He fills his tank to full capacity every time he meets a petrol station and keeps the receipts to give to his boss. **

**Q33.3 How much will his fuel receipts total for the single journey London to Paris? **

a. £43.29

b. £65.54

c. £72.78

d. £75.36

e. £81.76

**The courier's car breaks down in Paris and he is offered a choice between two replacement cars for his return journey to London: **

**• Car A runs on diesel, using 1 litre of diesel per 15 km. **

**• Car B runs on super, using 1 litre of super per 10 km. **

**The driver leaves on a full tank (45 litres for both cars) and decides to refuel to full capacity at every petrol station. **

**Q33.4 What is the differ-ence in fuel spend between the two options? **

a. €22.05

b. €23.13

c. €24.21

d. €25.03

e. €26.05

** The courier sets out from London in his usual car on a full tank of unloaded. On the way he stops at a petrol station to fill his fuel tank completely. The refuelling costs him €28.75 (or Pound Sterling equivalent). **

**Q33.5 How many litres of unleaded did he buy? **

a. 8 litres

b. 23 litres

c. 26 litres

d. 27 litres

e. 41 litres

**Answer and Explanation**

**Q33.1 - d: 5h 41min **

The UK leg of the journey is 130 km. The French leg of the journey is 300 km. The journey time is therefore: 130/110 + 300/120 + 2 hours (ferry) = 5.681818 hours i.e. 5 hours and 41 minutes.

**Q33.2 - b: 20 km **

The fuel tank has a capacity of 45 litres, which will enable the courier to drive a distance of 45 x 10 = 450 km. The total distance from London to Paris is 430 km. Therefore he will be able to get to Paris safely but will run out of petrol 20 km thereafter.

**Q33.3 - b: £65.54**

The courier starts with a tank containing 20 litres of fuel. By the time he reaches the first petrol station, he will have travelled 80 km and therefore used 80/10 = 8 litres, leaving 12 litres in the tank. He therefore needs a top up of 45-12 = 33 litres. The cost is 33 x 89p = £29.37.

By the time he reaches the second petrol station, he will have travelled 150 km, using 15 litres. Refuelling will cost 15 x 1.25 / 1.20 = £15.62.

He then needs to travel 180 km and therefore use 18 litres of fuel to get to the final petrol station, where refuelling costs 18 x 1.37 / 1.20 = £20.55. The total spend equals £29.37 + £15.62 + £20.55 = £65.54.

**Q33.4 - b: €23.13 **

The spend for Car A Is calculated as follows: (20/15) x 0.95 + (180/15) x 0.87 + (150/15) x (0.99x1.20) = E23.59. The spend for Car B is calculated as follows: (20/10) x 1.76 + (180/10) x 1.47 + (150/10) x (0.93x1.20) = £46.72.

The difference is €23.13.

**Q33.5 - b: 23 litres **

There are only 3 possibilities for refuelling on the way:

• Between London and Dover: this would only be for 8 litres and would cost £7.12, well below the E28.75 that he paid.

• At the petrol station after Calais: this would be for 23 litres, calculated as (80+50+100)/10. It would cost 23 x E1.25 = €28.75 (the answer we are looking for).

• At the petrol station before Paris, this would be for 41 litres and would cost 41 x €1.37 = E56.17.

Another way to get to the answer is to spot that, roughly speaking, a litre of unleaded will cost between el and €1.4. A cost of E28.75 would therefore mean a refuelling of between 20 and 29 litres. This can only happen at the middle petrol station. At that petrol station the refuelling would need to be for 23 litres in view of the distance driven to get there and the consumption of 1 litre per 10km.

Drafted by Juno Wong(UCAT Prep)