IGCSE · Mathematics 0580 · Number

Rates: IGCSE Mathematics questions with answers

Free Rates questions for IGCSE Mathematics (0580), part of Number. Each question has the answer and the marking points an examiner would look for.

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Rates practice questions

Question 1Structured · 3 marksA* challenge

Tap A can fill a tank in 3 hours. Tap B can fill the same tank in 15 hours.
Both taps are turned on together to fill the empty tank.
How long does it take to fill the tank? Give your answer in hours and minutes.

[3]
Show answers and mark scheme
PartAnswer and marking pointsMarks
2 hours 30 minutes
13 + 115 per hour M1
= 1845 so time = 4518 h A1
2 hours 30 minutes A1
3
Question 2Structured · 8 marksA* challenge

The minute hand of a clock turns through 6° each minute and the hour hand through 0.5° each minute.

(a)

Find the two times between 4 o’clock and 5 o’clock when the hands are at right angles. Give each time to the nearest second.

[6]
(b)

How many times from one midnight up to, but not including, the next midnight do the hands point in exactly the same direction?

[2]
Show answers and mark scheme
PartAnswer and marking pointsMarks
(a)4:05:27 and 4:38:11
at 4:00 the angle is 120° B1
relative speed 5.5° per minute B1
120 − 5.5t = 90 M1
t = 5511 min → 4:05:27 A1
5.5t − 120 = 90 M1
t = 38211 min → 4:38:11 A1
6
(b)22
minute hand gains a full turn every 72011 minutes M1
22 A1
2
Question 3Structured · 4 marks
(a)

A train travels 390 km in 3 hours 15 minutes. Calculate its average speed in km/h.

[2]
(b)

Change this speed into metres per second.

[2]
Show answers and mark scheme
PartAnswer and marking pointsMarks
(a)120 km/h
3 h 15 min = 3.25 h M1
120 A1
2
(b)33.3 m/s
× 1000 ÷ 3600 M1
33.3 A1
2
Question 4Structured · 4 marksA* challenge

A coach travels 90 km at an average speed of 72 km/h. It then stops for 20 minutes. It then travels 40 km at an average speed of 50 km/h.
Calculate the average speed for the whole journey, including the stop.

[4]
Show answers and mark scheme
PartAnswer and marking pointsMarks
54.5 km/h
90 ÷ 72 = 1.25 h and 40 ÷ 50 = 0.8 h M1
total time = 2.38 h (stop = 20 ÷ 60) M1
130 ÷ 2.383 M1
54.5 A1
4
Question 5Structured · 3 marksA* challenge

Tap A can fill a tank in 4 hours. Tap B can fill the same tank in 12 hours.
Both taps are turned on together to fill the empty tank.
How long does it take to fill the tank? Give your answer in hours and minutes.

[3]
Show answers and mark scheme
PartAnswer and marking pointsMarks
3 hours
14 + 112 per hour M1
= 1648 so time = 4816 h A1
3 hours A1
3
Question 6Structured · 4 marks
(a)

A train travels 157.5 km in 1 hour 45 minutes. Calculate its average speed in km/h.

[2]
(b)

Change this speed into metres per second.

[2]
Show answers and mark scheme
PartAnswer and marking pointsMarks
(a)90 km/h
1 h 45 min = 1.75 h M1
90 A1
2
(b)25 m/s
× 1000 ÷ 3600 M1
25 A1
2

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Original Cambridge-style practice questions written for mentorriyaz.in. These are not Cambridge past paper questions, and this site is not affiliated with or endorsed by Cambridge University Press & Assessment. Updated 2026-11-04. Paper generator · mentorriyaz.in