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Algebra
Question

Mrs Tan cycles daily to work every day. The distance between his workplace and his home is 35 km. He cycles at a speed of $$x$$ km/h while going to work and increases his speed by 3 km/h when returning from work.

(a) Find the time he takes to travel to work in terms of $$x$$.

(b) Find the time he takes to return from work in terms of $$x$$.

(c) Given that he takes 20 minutes less while returning from work, show that his journey can be expressed by $$x^2+3x-315=0$$

(d) Solve $$x^2+3x-315=0$$

(e) Hence, find the speed when he is going to work.

(a) $$\frac{35}{x}$$
(b) $$\frac{35}{x+3}$$
(c) $$\frac{35}{x}-\frac{35}{x+3}=\frac{1}{3}$$
(d) $$x=\frac{-3+3\sqrt{141}}{2}$$
(e) $$16.31$$