How to Solve Time, Speed & Distance Problems

Solve Grade 12 time, speed and distance problems with the d = s × t triangle — define variables, write the equation, solve, check units. Worked CAPS example.

Time, speed and distance questions are pure algebra disguised as word problems. The whole topic reduces to one relationship: distance = speed × time. Everything else is rearrangement.

Steps

  1. Write down d = s × t. From it you get s = d / t and t = d / s. That's all the formulas you need.
  2. Define a variable for the unknown. Pick the quantity the question asks for and call it x (or t, s, d).
  3. Express every other quantity in the same units. Convert km/h to m/s or hours to minutes BEFORE substituting. Most marks are lost here.
  4. Set up the equation from the scenario. Equal distances, total times, or difference in times — whichever the question describes.
  5. Solve and check the units of the answer. If you wanted km/h and you got hours, you rearranged the wrong formula.

Worked example

A taxi travels 120 km at an average speed of 80 km/h. How long does the trip take?

  1. Use t = d / s.
  2. t = 120 / 80 = 1.5 hours = 1 hour 30 minutes.
  3. Check units: km ÷ km/h = h ✓.

Common mistakes

  • Mixing km/h with minutes without converting.
  • Using average speed = (s₁ + s₂) / 2 — that's only true when the two times are equal, not the two distances.
  • Forgetting to add stopping time to total trip time.

Exam tips

  • Draw a tiny d-s-t triangle in the margin. Cover the quantity you want and the formula stares back at you.
  • Always convert to consistent units (SI: metres and seconds, or km and hours) before substituting.
  • Write the unit next to every value and convert everything to the same unit before you calculate.

Frequently asked questions

Is the formula d = s × t on the CAPS formula sheet?

No — you're expected to know it. It's assumed background knowledge from Grade 8–9 onwards.

What is average speed when two distances are equal?

Average speed = 2·s₁·s₂ / (s₁ + s₂) — the harmonic mean of the two speeds.

How do I convert minutes to hours?

Divide by 60: 45 minutes is 45 ÷ 60 = 0,75 hours.

What formula links speed, distance and time?

Speed = distance ÷ time. A car covering 150 km in 2,5 hours averages 150 ÷ 2,5 = 60 km/h.

How do I convert between hours and minutes?

Multiply hours by 60 to get minutes and divide minutes by 60 to get hours. For example, 2.25 hours is 2 hours 15 minutes, because 0.25 × 60 = 15.

How do I find the average speed for a journey in two parts?

Divide the total distance by the total time; don't average the two speeds. 60 km at 60 km/h and 60 km at 120 km/h take 1.5 hours in total, so the average speed is 120 ÷ 1.5 = 80 km/h, not 90 km/h.

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