Chapter 39: Inverse Proportion

✏️ Explanation

In inverse proportion, as one quantity increases, another decreases. If y is inversely proportional to x, then xy = k (constant).

Speed and time, workers and completion time, and many physics relationships follow inverse proportion.

🧭 See chart: "Inverse Proportion Guide" (to be added)

4 workers complete a job in 6 hours. How long for 8 workers?

Step 1: Find the total work needed

Total work = 4 × 6 = 24 worker-hours

Step 2: Calculate time for 8 workers

Time for 8 workers = 24 ÷ 8 = 3 hours

workers take hours

How long for workers?

Result:

3 hours

Working: Total work = 24 worker-hours, so 8 workers take 3 hours

1. 5 machines produce 100 items in 2 hours. How long for 10 machines?

Time for 10 machines: hours

2. It takes 3 hours to travel 180km at 60km/h. How long at 90km/h?

Time at 90km/h: hours

3. 6 people share £240 equally. How much if 8 people share?

Each person gets: £

4. If y is inversely proportional to x, and y = 12 when x = 4, find y when x = 6.

y =

5. 2 pumps empty a pool in 5 hours. How long with 5 pumps?

Time with 5 pumps: hours

Inverse proportion: as one goes up, the other goes down. Find the constant (k = xy).