Town $P$ is $200$ km due north of Town $Q$. A van travels from Town $P$ at a constant speed

Question

Town $P$ is $200$ km due north of Town $Q$. A van travels from Town $P$ at a constant speed of $80$ km/h due west. At the same time, a lorry travels at a constant speed of $60$ km/h due south from Town $Q$. If the van and lorry travelled for $t$ hours, write down in terms of $t$, the distance of the van from Town $P$ after $t$ hours, the lorry from Town $P$ after $t$ hours. Given that after $t$ hours, the vehicles are $300$ kilometres apart, show that $5{{t}^{2}}+12t-25=0$. Solve the equation $5{{t}^{2}}+12t-25=0$, giving your answers correct to $2$ decimal places.

Accepted Answer

(a)(i) 80t km; (a)(ii) 60t + 200 km; (b) 5t^2 + 12t - 25 = 0; (c) t = 1.34 or -3.74.

Vehicles Travelling from Two Towns: A Quadratic Equation Problem

Vehicles Travelling from Two Towns: A Quadratic Equation Problem

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