Gilbert cycled at a speed of $\left( x+4 \right)$ km/h for $2x$ hours. He then jogged at a

Question

Gilbert cycled at a speed of $\left( x+4 \right)$ km/h for $2x$ hours. He then jogged at a speed of $\left( x-2 \right)$ km/h for $x$ hours. If the total distance he travelled is $45$ km, find an expression for the distance he cycled. an expression for the distance he jogged. Hence or otherwise, form an equation in $x$ and shows that it reduces to ${{x}^{2}}+2x-15=0$. Solve the equation ${{x}^{2}}+2x-15=0$ and state the reason why one of the values of $x$ is rejected. Hence, or otherwise, find the average speed for Gilbert’s journey.

Accepted Answer

(a) $2x^2+8x\text{ km}$ (b) $x^2-2x\text{ km}$ (c) $x^2+2x-15=0$ (d) $x=3$ (e) $5\text{ km/h}$

Quadratic Equation from a Distance–Speed–Time Problem

Quadratic Equation from a Distance–Speed–Time Problem

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