https://file.aiquickdraw.com/mathbot/file/17272047990868l9olzv2.jpg

Let's analyze and solve the problem.

### Given:
- Liam takes 56 minutes to fit 4 tyres to a van.

### Part a) 
How long would it take him to fit 12 tyres to three vans?

We know that Liam takes 56 minutes to fit 4 tyres. To fit 12 tyres, we can set up a proportion based on the time per tyre.

Time per tyre:
\[
\text{Time per tyre} = \frac{56 \, \text{minutes}}{4 \, \text{tyres}} = 14 \, \text{minutes per tyre}
\]

For 12 tyres:
\[
12 \, \text{tyres} \times 14 \, \text{minutes per tyre} = 168 \, \text{minutes}
\]
So, it will take Liam **168 minutes** to fit 12 tyres to three vans.

### Part b)
If he works for 42 minutes, how many tyres can he fit?

Since he fits 1 tyre in 14 minutes, the number of tyres he can fit in 42 minutes is:
\[
\frac{42 \, \text{minutes}}{14 \, \text{minutes per tyre}} = 3 \, \text{tyres}
\]

So, Liam can fit **3 tyres** in 42 minutes.

---

Would you like more detailed steps or explanations on any part? Here are 5 related questions for further practice:

1. How long would it take Liam to fit 8 tyres?
2. If Liam works for 70 minutes, how many tyres can he fit?
3. How many tyres can Liam fit in 3 hours?
4. How long would it take Liam to fit 20 tyres?
5. If Liam takes 10 minutes longer per tyre, how long would it take to fit 4 tyres?

**Tip:** When solving proportional problems, breaking down the rate per unit (like time per tyre) helps simplify calculations.

Liam is a tyre fitter. It takes him 56 minutes to fit 4 tyres to a van. 
a) How long would it take him to fit 12 tyres to three vans? 
b) If he works for 42 minutes, how many tyres can he fit?

Learn how to calculate the time it takes to fit 12 tyres and how many tyres can be fitted in 42 minutes using proportional reasoning and unit rates. Suitable for Grade 6-8 students.

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