Question 1
1(a) How long would it take you to travel 3 kilometres, if you walked at 6 km/h?
Give your answer in minutes.
ANSWER: Simple text answer
Answer: 30 mins
Workings:
Time = 3 \div 6 = 0.5 hours
30 minutes
Marks = 1
1(b)What is Laura’s average speed if she travels 126 miles in 2 hours?
ANSWER: Simple text answer
Answer: 63 mph
Workings:
Speed = 126 \div 2 = 63 mph
Marks = 1
1(c) Emma travels at a speed of 23 miles per hour for 3.5 hours.
How far has she travelled?
Give your answer in miles.
ANSWER: Simple text answer
Answer: 80.5 miles
Workings:
Distance = 23 \times 3.5 = 80.5 miles
Marks = 1
Question 2
2(a) A car journey of 214 miles took Jack a total 7 hours and 15 minutes to complete.
Calculate his average speed across the journey to 2 decimal places.
You must state the units.
ANSWER: Simple text answer
Answer: 29.52 mph
Workings:
Speed = 214 \div 7.25 = 29.52 mph
Marks = 2
2(b) Jack completed the return journey in half the time.
What was his average speed on the return journey?
ANSWER: Simple text answer
Answer: 59.03448 mph
Workings:
Speed = 214 \div 3.625 = 59.03448 mph
Marks = 1
Question 3
3(a) Nabeela travelled to London by train, her journey was made up of two parts.
One train into York and then another train into London.
The first train departed at 07:05 and the journey lasted for 12 minutes.
The second train departed at 07:27 and the journey lasted for 122 minutes.
The total distance travelled was 197 miles.
What was Nabeela’s average speed for the entire journey?
ANSWER: Simple text answer
Answer: 82.08 mph
Workings:
Total duration = 122 + (07:27 - 07:05) = 144 minutes = 2h 24m
2h 24[/latex]m = 2.4 hours
Average speed = 197 \div 2.4 = 82.08 mph (to 2 dp)
Marks = 2
3(b) York to London is a distance of 175 miles.
How many miles an hour faster was the first part of the journey?
ANSWER: Simple text answer
Answer: 23.93 mph
Workings:
First journey distance=(197-175) = 22 miles
First journey time =12 minutes =0.2 hours
First journey speed = 22 \div 0.2 = 110 mph
Second journey speed = 175 \div 2.03 = 86.07 mph (to 2d.p.)
110-86.07 = 23.93 mph
Marks = 3
Question 4
Trihao is driving from Cambridge to London.
Assume the distance between Cambridge and London is 100 km.
4(a) Given that Trihao drives at an average speed of 80 km/h, work out his journey time.
Give your answer in hours.
ANSWER: Simple text answer
Answer: 1.25 hours
Workings:
Time = \dfrac{Distance}{Speed} = \dfrac{100}{80} = 1.25 hours
Marks = 2
4(b) Chris instead decides to take the train.
He leaves Cambridge at the same time as Trihao, but arrives in London 20 minutes before Trihao arrives.
Calculate the average speed of the train.
ANSWERS:
Answer: 109 km/h
Workings:
Time is 55 minutes = 0.917 hours
Speed = \dfrac{Distance}{Time} = \dfrac{100}{0.917} =109 km/h
Marks = 2
Question 5
5(a) Jordan finishes college at 16:30 h.
He walks to the his mum’s work 0.24 km away, at a speed of 2 km/h.
He waits there 7 minutes for his mum to finish work before she drives them both 7 km back home at an average speed of 26 km/h.
What time does Jordan arrive home?
Give your answer to the nearest minute.
ANSWER: Simple text answer
Answer: 17:00
Workings:
Time from college to work = (0.24 \div 2) \times 60 = 7.2 minutes
Waiting time =7 minutes
Driving time = 7 \div 26 = 0.2692 hours =16.15 minutes
So arrival time = 16:30h + (7m + 16.15m + 7.2m) = 17:00h to the nearest minute.
Marks = 3
5(b) If Jordan jogs the 7.1 km directly home at a speed of 7.4 km/h, at what time would he arrive home?
Give your answer to the nearest minute.
ANSWER: Simple text answer
Answer: 17:28
Workings:
Time to jog = 7.1 \div 7.4 = 0.9595h
16:30h + 0.95h (58 minutes) =17:28h
Marks = 2
Question 6
Anna needs to be at the museum for the open evening at 18.00 h.
She will walk to the museum from the bus depot at a speed of 3 mph.
To arrive at the bus depot she will catch the bus at the stop from near her house. The bus travels at an average speed of 25 mph.
On the walk from her house to the bus stop she will average a speed of 6 mph.
The bus depot is 0.7 miles from the museum.
The bus journey from bus stop to bus depot is 2.2 miles.
The walk from her house to the bus stop is 0.3 miles.
Buses leave the bus stop at 15 minute intervals starting from 07:00 h.
6(a) What time is the latest bus Anna can catch whilst still arriving at the museum on time?
ANSWER: Simple text answer
Answer: 17:30
Workings:
Time from Depot to Museum = 0.7 \div 3 = 0.23 h =14 minutes
Time from Bus Stop to Depot = 2.2 \div 25 = 0.088h = 5.28 minutes = 5minutes 16 seconds
18:00h - 14m - 5m16s = 17:40h 44seconds
Bus prior to this is 17:30
Marks = 4
6(b) What time should Anna leave her house to catch the bus?
ANSWER: Simple text answer
Answer: 17:27
Workings:
Time = \dfrac{distance}{speed} = \dfrac{0.3 \space miles}{6 \space mph} = 0.05 hours = 3 minutes
17:30h - 3 minutes = 17:27h
Marks = 2
Question 7
7(a) Mrs Smith travels on Plane M, which flies at an average speed of 825 km/h for 7 hours and 24 minutes from Location A to Location B.
She then waits at Location B for 2 hours and 11 minutes, before flying to Location C on Plane N, which flies at an average speed of 722 km/h for 4 hours and 48 minutes.
Both planes fly in a straight line to their respective destinations.
What is the total distance of her journey?
Give your answer to 1 decimal place.
ANSWER: Simple text answer
Answer: 9570.6 km
Workings:
Distance from A to B = 825 \times 7.4 = 6105 km
Distance from B to C = 722 \times 4.8 = 3465.6 km
Distance from A to B to C = 6105 + 3465.6 = 9570.6 km
Marks = 2
7(b) The journey from Location A to Location B to Location C is such that it forms a right angle at Location B.
Plane Z flies directly from Location A to Location C at a speed of 795km/h
If Plane Z leaves Location A at 11.53 h, what time does it arrive at Location C?
ANSWER: Simple text answer
Answer: 20:42h
Workings:
AC = \sqrt{(6105^2 + 3465.6^2 )} = 7020.07
Time = 7020.07 \div 795 = 8.83 h ≈ 8h 49m
Arrival Time =11:53h + 8h 49m =20:42h
Marks = 2