Theory question 107
Linear and Simultaneous Equations(a) On a certain day, Mabel rode her bicycle for 45 minutes and then walked for 1 hour, covering a total distance of 10.4 km. The average cycling speed is three times the walking speed.
(i) Find, correct to two significant figures, the walking speed
(ii) If Mabel increases the average cycling speed by 20% but maintains the walking speed for 1 hour, find, in minutes, the new cycling time
(b) A line, L passing through K(−3, 5) is parallel to the equation 3x − 2y + 5 = 0. Find the equation of L.
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(a)(i) Walking speed w: ¾ × 3w + w = 10.4 ⇒ 3.25w = 10.4 ⇒ w = 3.2 km/h
(ii) New cycling speed = 9.6 × 1.2 = 11.52 km/h; walking covers 3.2 km, so cycling distance = 7.2 km
Time = 7.2 ÷ 11.52 = 0.625 h = 37.5 minutes
(b) 2y = 3x + 5 ⇒ gradient 3/2; y − 5 = 3/2(x + 3) ⇒ 3x − 2y + 19 = 0
Parallel lines have the same gradient.