**Solution:** The correct answer is 1.5.

**Short Trick Explanation:**

– **Cycling**: Speed is 8.5 km/h for 4 hours. Compared to the average speed of 10 km/h, the difference is \(10 – 8.5 = 1.5\) km/h. Over 4 hours, the difference contributes to a total “speed deficit” of \(1.5 \times 4 = 6\) km.

– **Auto**: Speed is 20 km/h for 1.5 hours. Compared to the average speed of 10 km/h, 1.5*10=15km 20km-15km=5km

– **Walking**: Speed is 4 km/h. Compared to the average speed of 10 km/h, the difference is \(10 – 4 = 6\) km/h. For \(y\) hours, this results in a “speed deficit” of \(6 \times y\) km.

**Equation**:

\[

-6 + 5 – 6y = 10

\]

Simplify to find \(y\):

\[

6y = 9

\]

\[

y = \frac{9}{6} = 1.5 \text{ hours}

\]

Therefore, the value of \(y\) is 1.5 hours.

**Explanation:**

– **Step 1:** Calculate the distance covered in each phase of the journey:

– Cycling: \( \text{Distance} = 8.5 \text{ km/h} \times 4 \text{ hours} = 34 \text{ km} \)

– Auto: \( \text{Distance} = 20 \text{ km/h} \times 1.5 \text{ hours} = 30 \text{ km} \)

– Walking: \( \text{Distance} = 4 \text{ km/h} \times y \text{ hours} = 4y \text{ km} \)

– **Step 2:** Calculate the total distance and total time:

– Total Distance \( = 34 + 30 + 4y = 64 + 4y \text{ km} \)

– Total Time \( = 4 + 1.5 + y = 5.5 + y \text{ hours} \)

– **Step 3:** Use the average speed formula:

– Given average speed = 10 km/h

– \( \text{Average Speed} = \frac{\text{Total Distance}}{\text{Total Time}} \)

– \( 10 = \frac{64 + 4y}{5.5 + y} \)

– **Step 4:** Solve the equation for y:

– \( 10 \times (5.5 + y) = 64 + 4y \)

– \( 55 + 10y = 64 + 4y \)

– \( 10y – 4y = 64 – 55 \)

– \( 6y = 9 \)

– \( y = 1.5 \)

Therefore, the value of y is 1.5 hours.