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WAEC 2023 · Paper 2 · Q1

  1. (a)

    A car travels a distance of 112 km112\text{ km} at an average speed of 70 km/h70\text{ km/h}. It then travels further for 60 km60\text{ km} at an average speed of 50 km/h50\text{ km/h}. Calculate, for the entire journey, the total time taken (in hours).

  2. (b)

    If xy=2\dfrac xy = 2 and yz=3\dfrac yz = 3, find the value of x+yy+z\dfrac{x + y}{y + z}.

Worked solution (try it first)

(a)

  1. Time =distancespeed= \frac{\text{distance}}{\text{speed}} for each part of the journey.
  2. First part: 11270=1.6\frac{112}{70} = 1.6 hours.
  3. Second part: 6050=1.2\frac{60}{50} = 1.2 hours.
  4. Total time =1.6+1.2=2.8= 1.6 + 1.2 = 2.8 hours (2 hours 48 minutes).

(b)

  1. From yz=3\frac yz = 3, y=3zy = 3z.
  2. From xy=2\frac xy = 2, x=2y=6zx = 2y = 6z.
  3. So x+yy+z=6z+3z3z+z\frac{x + y}{y + z} = \frac{6z + 3z}{3z + z}
    =9z4z= \frac{9z}{4z}
    =94= \frac94
    =214= 2\frac14.

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