**UCAT Question Analysis - Quantitative Reasoning Question 30**

Recently published statistics show that, on some lines, trains run more slowly than 20 years ago.

The average journey times for three major lines were as follows:

For the purpose of this exercise, you should assume that none of the trains stopped at any of the intermediary stations shown In the table above, i.e. assume that all trains ran non-stop from their city of origin to London.

**Q30.1 Now much longer did the Lewes to London Victoria journey take in 2008 as compared to 1987?**

a. 5 min

b. 8 min

c. 25 min

d. 61 min

e. 66 min

**Q30.2 What was the average speed of the Canterbury East to London Vic-toria train In 1987 over the whole line (to the nearest km/h)?**

a. 47 km/h

b. 58 km/h

c. 65 km/h

d. 76 km/h

e. 81 kmlh

**Q30.3 By what proportion did the journey time increase between South-end and London Fenchurch Street between 1987 and 2008?**

a. 9.00%

b. 9.26%

c. 10.00%

d. 10.20%

e. 10.26%

**Q30.4 The train company's executives think that, in future, they can make the Canterbury East to London Victoria train journey as short as it used to be in 1987 by allowing their trains to run faster on the Fa-versham to Chatham portion of the route (with the times for the other two portions of the mute remaining at 2008 levels).**

**At what speed would the train need to run on the Faversham to Chatham portion in order for the whole journey to last the same amount of time as in 1987?**

a.43.2 km/h

b.54.0 km/h

c.69.5 km/h

d.86.9 km/h

e.89.6 km/h

**030.5 The price of a Canterbury East to London Victoria ticket is £15.90. We are told that the price of a ticket on the Lewes to Victoria line is, on a pound per mile basis, the same as a Canterbury East to Lon-don Victoria ticket. Given that a ticket on the Lewes to London Vic-toria line costs £12.40, what Is the distance between Lewes and London Victoria (to the nearest mile)?**

a. 50 miles

b. 55 miles

c. 61 miles

d. 66 miles

e. 82 miles

**Answer and Explanation**

**Q30.1 — b: 6 minutes**

The additional journey time is 5 minutes for the first part of the journey (20 — 15) plus 1 minute for the second part of the journey (14 — 13). The final two parts took the same amount of time in both years.

**Q30.2 — d: 76 km/h**

The total distance was 12 + 18 + 34 = 64 miles. This was travelled in 13 + 25 + 43 = 81 minutes (or 81/60 hours). The average speed was therefore: 64 x 1.6093 / 81 x 60 = 76 km/h.

**Q30.3 — d: 10.20%**

The journey time in 1987 on the Southend to Fenchurch Street line was 49 minutes. In 2008, it was 54 minutes. This represents an increase of 54 / 49 = 1.102, i.e. 10.2%

**Q30.4 — d: 86.9 km/h**

In 1987, the total journey time was 5 minutes less than in 2008. We are told that this time must he recovered on the Faversham to Chatham portion of the route and therefore this part of the journey (18 miles) will need to be done in 20 minutes instead of 25 minutes. 18 miles in 20 minutes is equiv-alent to 54 miles in an hour. Converting to kilometres (x 1.6093) gives a speed of 86.9 km/h.

**Q30.5 — a: 50 miles**

The number of miles on the Canterbury to Victoria Line is 64. Therefore the cost on a pound per mile basis is calculated as 15.90 / 64 = £0.2484375.

A ticket on the Lewes to Victoria line costs £12.40. Since the cost on a pound per mile basis is the same on both lines, the number of miles on the Lewes to Victoria line is 12.40 / 0.2484375 = 49.91 miles (rounded up to 50 miles).