Respuesta :
ANSWER
2h 30min
EXPLANATION
The average speed of an object is:
[tex]v=\frac{\Delta x}{\Delta t}[/tex]We know that plane x's speed is 800mph and plane y's is 400mph. We want to find at what time they will be in the same position:
[tex]\Delta x=v\cdot\Delta t[/tex]So we have to solve:
[tex]\begin{gathered} \Delta x_X=\Delta x_Y \\ v_X\cdot\Delta t_X=v_Y\cdot\Delta t_Y \end{gathered}[/tex]Remember that plane y had a 2.5 hour head start, so time between these two planes is:
[tex]\Delta t_Y=\Delta t_X+2.5h[/tex]To simplify the equation, let's call Δt_X = t. So the equation to solve is:
[tex]\begin{gathered} v_X\cdot t=v_Y\cdot(t+2.5h) \\ 800\text{mph}\cdot t=400\text{mph}\cdot(t+2.5h) \end{gathered}[/tex]First apply distributive property on the right side of the equation:
[tex]\begin{gathered} 800\cdot t=400\cdot t+400\cdot2.5 \\ 800\cdot t=400\cdot t+1000 \end{gathered}[/tex]Subtract 400t from both sides of the equation:
[tex]\begin{gathered} 800t-400t=400t-400t+1000 \\ 400t=1000 \end{gathered}[/tex]And divide both sides by 400:
[tex]\begin{gathered} 400\cdot\frac{t}{400}=\frac{1000}{400} \\ t=2.5 \end{gathered}[/tex]So the time it will take for plane x to overtake plane y is another 2 hours and 30 minutes
