MHB Quadratic application question what was the jets speed from Bangkok to Tokyo

[Wild ownz al]

Hey this Quadratic application question is giving me trouble.

A jet flew from Tokyo to Bangkok, a distance of 4800km. On the return trip, the speed was decreased by 200km/h. If the difference in the times of the flights was 2 hours, what was the jets speed from Bangkok to Tokyo?

Just need the formula for the Jets speed and I should be fine with the rest.

This was my guess: 4800 = (x-200)(-2x)

 

[MarkFL]

Hey this Quadratic application question is giving me trouble.

A jet flew from Tokyo to Bangkok, a distance of 4800km. On the return trip, the speed was decreased by 200km/h. If the difference in the times of the flights was 2 hours, what was the jets speed from Bangkok to Tokyo?

Just need the formula for the Jets speed and I should be fine with the rest.

This was my guess: 4800 = (x-200)(-2x)

Hello, and welcome to MHB! (Wave)

I've moved your question to its own thread.

I would use the fact that time is distance per average speed. Let distances be measured in km and time in hrs. Let \(v\) be the plane's speed from Bangkok to Tokyo.

$$t-2=\frac{4800}{v+200}$$

$$t=\frac{4800}{v}$$

Now, these equations imply:

$$t=\frac{4800}{v+200}+2=\frac{4800}{v}$$

Multiply through by \(v(v+200)\):

$$4800v+2v(v+200)=4800(v+200)$$

Distribute after dividing through by 2, then collect like terms and arrange in standard form:

$$v^2+200v-480000=0$$

Factor:

$$(v+800)(v-600)=0$$

Discarding the negative root, we find:

$$v=600$$

Does this make sense?

 

[Wild ownz al]

AMAZING you are brilliant. Thank you :)

 

[Wild ownz al]

AMAZING you are brilliant. Thank you :)

If the plane's speed is "decreased" by 200km/h then shouldn't it be (v - 200) instead of (v + 200)?

Also if you ended up with two roots how do you know which one is the planes speed?

 

[MarkFL]

If the plane's speed is "decreased" by 200km/h then shouldn't it be (v - 200) instead of (v + 200)?

The first equation represents the first leg of the journey, from Tokyo to Bangkok. But, \(v\) represents the speed on the second leg, the return trip, where the speed has been decreased by 200. And so the speed on the first leg must be \(v+200\).

Also if you ended up with two roots how do you know which one is the planes speed?

Speed, in order to have any meaning, must be positive (it is a magnitude like distance), and so we discard the negative root.