Theory question 103
Linear and Simultaneous Equations(a) Solve the simultaneous equations: 1/x + 1/y = 5; 1/y − 1/x = 1.
(b) A man drives from Ibadan to Oyo, a distance of 48 km in 45 minutes. If he drives at 72 km/h where the surface is good and 48 km/h where it is bad, find the number of kilometres of good surface.
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Model answer
(a) Adding: 2/y = 6, so y = ⅓. Then 1/x = 5 − 3 = 2, so x = ½.
(b) Let x km be good surface: x/72 + (48 − x)/48 = ¾.
Multiply by 144: 2x + 3(48 − x) = 108 → 144 − x = 108 → x = 36 km.
Explanation
Time = distance ÷ speed for each part; the times add to 45 minutes = ¾ hour.