Speed, Distance, Time Textbook Exercise - Corbettmaths - Free Printable

Here are the solutions to the questions on the worksheet.

Question 1

*Convert the times from hours/minutes into hours, without a calculator.*

To do this, remember that there are 60 minutes in an hour. You divide the minutes by 60 to get the decimal part.
* 15 mins $\div$ 60 = 0.25
* 30 mins $\div$ 60 = 0.5
* 45 mins $\div$ 60 = 0.75
* 20 mins $\div$ 60 = $1/3$ or approx 0.33 (usually written as a fraction or recurring decimal in non-calc contexts, but here likely looking for simple decimals where possible. Let's look at the others. 20/60 is 1/3. Let's provide fractions/recurring if needed, but standard GCSE usually accepts 0.33... or just the fraction. However, looking at the examples, they use decimals. Let's stick to exact decimals where possible, or standard fractions converted. Actually, 20 mins is often left as $0.\dot{3}$ or just used in calculation. Let's provide the decimal equivalent.)

Let's solve each one:

(a) 15 minutes: $15 \div 60 = 0.25$ hours
(b) 30 minutes: $30 \div 60 = 0.5$ hours
(c) 45 minutes: $45 \div 60 = 0.75$ hours
(d) 20 minutes: $20 \div 60 = 0.333...$ (or $1/3$) hours. *Note: In many school contexts without a calculator, you might leave this as a fraction $\frac{1}{3}$ or write $0.\dot{3}$. If a decimal is strictly required, it is approximately 0.33.*
(e) 40 minutes: $40 \div 60 = 0.666...$ (or $2/3$) hours. *Similarly, this is $0.\dot{6}$ or approx 0.67.*
(f) 2 hours 30 minutes: The 2 stays as 2. The 30 mins is 0.5. Total = 2.5 hours
(g) 1 hour 15 minutes: The 1 stays as 1. The 15 mins is 0.25. Total = 1.25 hours
(h) 3 hours 45 minutes: The 3 stays as 3. The 45 mins is 0.75. Total = 3.75 hours
(i) 2 hours 40 minutes: The 2 stays as 2. The 40 mins is $0.666...$ Total = 2.666... (or $2\frac{2}{3}$) hours
(j) 5 hours 30 minutes: The 5 stays as 5. The 30 mins is 0.5. Total = 5.5 hours
(k) 7 hours 20 minutes: The 7 stays as 7. The 20 mins is $0.333...$ Total = 7.333... (or $7\frac{1}{3}$) hours
(l) 4 hours 15 minutes: The 4 stays as 4. The 15 mins is 0.25. Total = 4.25 hours

*(Self-Correction for Q1 d, e, i, k: Since the prompt says "without a calculator" and gives examples like 0.75, it implies exact decimals. However, 20 and 40 minutes do not result in terminating decimals. In UK Maths (Corbettmaths), these are often accepted as fractions like $1/3$ or recurring decimals. I will provide the recurring decimal notation or fraction for clarity).*

Question 2

*Convert the times from hours/minutes into hours. You may use a calculator if needed.*

Here we divide the minutes by 60 using a calculator.

(a) 18 minutes: $18 \div 60 =$ 0.3 hours
(b) 54 minutes: $54 \div 60 =$ 0.9 hours
(c) 1 hour 3 minutes: $3 \div 60 = 0.05$. Total = 1.05 hours
(d) 1 hour 36 minutes: $36 \div 60 = 0.6$. Total = 1.6 hours
(e) 2 hours 48 minutes: $48 \div 60 = 0.8$. Total = 2.8 hours
(f) 2 hours 33 minutes: $33 \div 60 = 0.55$. Total = 2.55 hours
(g) 8 hours 51 minutes: $51 \div 60 = 0.85$. Total = 8.85 hours
(h) 3 hours 21 minutes: $21 \div 60 = 0.35$. Total = 3.35 hours
(i) 27 minutes: $27 \div 60 =$ 0.45 hours

Question 3

*Convert the times from hours/minutes into hours. Give each answer to 3 decimal places.*

*Note: The image cuts off the specific questions for Question 3. However, based on the pattern, here is how you would solve any question in this section:*

1. Take the minutes part.
2. Divide by 60.
3. Add the whole hours (if any).
4. Round the final number to 3 decimal places.

*Since there are no specific sub-questions (a, b, c...) visible for Question 3, I cannot provide specific answers for them. The work above covers all visible questions.*

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Final Answer:

Question 1:
(a) 0.25 hours
(b) 0.5 hours
(c) 0.75 hours
(d) $0.\dot{3}$ hours (or $1/3$ hours)
(e) $0.\dot{6}$ hours (or $2/3$ hours)
(f) 2.5 hours
(g) 1.25 hours
(h) 3.75 hours
(i) $2.6\dot{6}$ hours (or $2\frac{2}{3}$ hours)
(j) 5.5 hours
(k) $7.\dot{3}$ hours (or $7\frac{1}{3}$ hours)
(l) 4.25 hours

Question 2:
(a) 0.3 hours
(b) 0.9 hours
(c) 1.05 hours
(d) 1.6 hours
(e) 2.8 hours
(f) 2.55 hours
(g) 8.85 hours
(h) 3.35 hours
(i) 0.45 hours

Question 3:
(The specific questions for this section are not visible in the image provided.)