Question

Two trains depart from one station, one going north at $30.00$ miles per hour, and another going west, steadily accelerating with a rate of $0.3333$ miles per minute.
How many minutes after departure would the two trains be $50.00$ miles apart?

• A. $17.19min$
• B. $76.28min$
• C. $89.54min$
• D. $120.0min$
• E. $240.0min$

Answer 1

The correct option is A $17.19min$

Speed of the train going north is given by
$v_1=\frac{30}{60}miles/minute=0.5miles/min$
Let $t$ be the time when both trains are 50 miles apart, then the distance covered by northward going train is,
$d_1=v_{1}t=0.5tmiles$
Displacement of train going westwards at time $t$,
$d_2=\frac{1}{2}a{t}^{2}miles=\frac{1}{2}\times 0.3333t^{2}miles=0.1666t^{2}miles$
Now since the angle between the directions of both trains is ${90}^{\circ }$, the distance between them at time $t$ is given by
$d^2={d_1}^2+{d_2}^2{50}^2={\left(0.5t\right)}^2+{\left(0.1666t^2\right)}^{2}Let{t}^{2}bex,0.02775x^2+0.25x=25000.00111x^2+0.01x=100Solvingthequadraticequation,wegetx=295.6Thus,t=\sqrt{295.6}=17.19min$