WAEC 2024 · Paper 2 · Q2

Linear & simultaneous equations
Commercial arithmetic

A car travelled a distance of $(2x + 13)\text{ km}$ at $67.5\text{ km/h}$ and $(5x - 20)\text{ km}$ at $72\text{ km/h}$ . If the total time for the entire journey was 90 minutes, find the value of $x$ .

Worked solution (try it first)

Time $= \frac{\text{distance}}{\text{speed}}$ for each part, and 90 minutes $= 1.5$ hours: $\frac{2x + 13}{67.5} + \frac{5x - 20}{72} = 1.5$ .
Multiply every term by 1080 (which both 67.5 and 72 divide into: $1080 \div 67.5 = 16$ and $1080 \div 72 = 15$ ): $16(2x + 13) + 15(5x - 20) = 1620$ .
Expand: $32x + 208 + 75x - 300 = 1620$ .
So $107x - 92 = 1620$ , $107x = 1712$ and $x = 16$ .
Check: the distances are 45 km and 60 km, taking $\frac{45}{67.5} = \frac23$ h and $\frac{60}{72} = \frac56$ h, a total of $1\frac12$ h ✓.

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