Question 4 · Worked Example

The Greyhound Track

A rectangle with a half-circle stuck on each end. Let's crack it in 4 small steps.

1
Radius
2
Area
3
Lap time
4
Runner
STEP 1 · PART (a)

How big is the curved end?

120 m straight 120 m straight r = ?
Why we start here: the radius unlocks everything else — the area in Step 2 all depends on it. Get this right first.

The total track is 480 m. The two straight sides use up 2 × 120 = 240 m. Whatever is left belongs to the two curved ends. Put two semicircles together and you get one full circle — so that leftover length is the circle's circumference.

Formula → solve for r curves = 480 − (2 × 120) = 240 m circumference: 2 × π × r = 240 → r = 240 ÷ (2 × π) = 38.2 m
Answer (a)r ≈ 38.2 m
STEP 2 · PART (b)

What's the area inside?

RECTANGLE 120 × (2r) ½○ ½○
Why split it up: the shape looks weird, but it's really just a rectangle in the middle plus two half-circles on the ends. Two halves = one whole circle. Find each piece, then add.

Width of the rectangle = the diameter = 2 × 38.2 = 76.4 m. Now add the rectangle to the full circle.

Formula → two pieces, then add rectangle = 120 × 76.4 = 9167.32 circle = π × r² = π × 38.2² = 4583.66 → total = 9167.32 + 4583.66 = 13750.99 m²
Answer (b)Area ≈ 13750.99 m²
STEP 3 · PART (c)

How fast is one lap?

Why convert units first: the speed is in km per hour, but the answer wants seconds and the track is in metres. Match the units before dividing, or the numbers won't mean anything.

The dog runs 60 km/h. One lap is the full 480 m. Turn the speed into metres per second, then use time = distance ÷ speed.

🐕

A lap takes 28.8 s at this speed.

Formula → convert, then divide 60 km/h = 60000 m ÷ 3600 s = 16.67 m/s time = distance ÷ speed → 480 ÷ 16.67 = 28.8 s
Answer (c)≈ 28.8 seconds per lap
STEP 4 · PART (d)

Did Maura hit her goal?

Why this is the same trick: it's time = distance ÷ speed again — just compare the answer to her 2-hour target. Keep the units matching: metres and minutes.

Race = 21.1 km = 21100 m. Speed = 150 m/min. Goal = 2 hours = 120 min.

Formula → time, then compare time = 21100 ÷ 150 = 140.7 min that's 2 h 20.7 min → 140.7 min > 120 min goal
🏁 2 h goal
Startrunning…Finish
Answer (d)No — she misses it by ~20.7 min
🎉 ALL DONE

Quick recap

Four questions, one big idea: break a scary shape into pieces you already know, and always match your units before you divide.

1Radius of the ends38.2 m
2Area of the track13750.99 m²
3Time for one lap28.8 s
4Maura's 2-hour goalMissed ✗
Remember the two power moves: ① a full lap of the curves = the circumference of one whole circle. ② time = distance ÷ speed (with matching units).