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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) \(16.31\)

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