A tour bus covers 420 km at a uniform speed. If the speed were 10 km/h less, it would take 1 hour more. Find the speed of the bus.

How to lay out the answer. Follow the frame, then write it in your own words.

1 · Write what is given and what is to be found. Distance = 420 km. Let the speed be x km/h. To find: x.
2 · Write the formula. Time = distance ÷ speed. Time at x km/h = 420/x hours; at (x − 10) km/h = 420/(x − 10) hours.
3 · Form the equation. 420/(x − 10) − 420/x = 1
4 · Write it in standard form. Multiply by x(x − 10): 420x − 420(x − 10) = x(x − 10), so 4200 = x² − 10x, giving x² − 10x − 4200 = 0.
5 · Solve. D = (−10)² − 4(1)(−4200) = 100 + 16800 = 16900, √D = 130. x = (10 ± 130)/2, so x = 70 or x = −60.
6 · Reject and say what it means. Speed cannot be negative, so x = 70 km/h. The trip takes 6 hours at 70 km/h and 7 hours at 60 km/h.
7 · Check and box the answer. 7 − 6 = 1 hour more, as stated. Therefore the speed of the bus is 70 km/h.

Scoring tip: Write which time is longer before you subtract. The slower trip takes more time, so its time comes first.