Question

A plane takes off at 6:00 am, traveling north at 270 miles per hour. A jet takes off at 7:00 am, traveling north at 460 miles per hour. At what time will the jet overtake the plane? (Round your answer to the nearest minute.)

Answer 1

Answer:

The jet will overtake the plane at 8:25 am.

Step-by-step explanation:

The distance $D_p$ traveled by the plane after time $t$ since it took off is modeled by the equation

$D_p = 270t$

And the distance $D_j$ traveled by the jet after time $t$ since the plane took off is given modeled by the equation

$D_j =460t-460$    (we set this up such that at $t=1,$ $D_j= 0$)

Now, the jet will overtake the plane when $D_j> D_p$:

$460t-460> 270t$

$460t-270t> 460$

$190t>460$

$\boxed{t> 2.42\: hours }$

Which is 2 hours and 25 minutes after 6:00 am, or at 8: 25 am; therefore, the jet will overtake the plane at 8:25 am.

Answer 2

Answer:

the answer is 8:25

Step-by-step explanation: