WAEC 2021 · Paper 1 · Q32

Linear & simultaneous equations

A cyclist moved at a speed of $x\text{ km/h}$ for 2 hours. He then increased his speed by $2\text{ km/h}$ for the next 3 hours. If the total distance covered is $36\text{ km}$ , calculate his initial speed.

Worked solution (try it first)

Distance is speed times time.
The first stretch is $2x$ km.
The new speed is $x + 2$ for 3 hours, so the second stretch is $3(x + 2) = 3x + 6$ km.
The total is 36 km: $2x + 3x + 6 = 36$ , so $5x = 30$ .
Divide by 5: $x = 6$ .
His initial speed was $6\text{ km/h}$ , option D.

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