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

#### Wild ownz al

##### Member
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

Staff member
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!

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.

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

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

Now, these equations imply:

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

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

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

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

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

Factor:

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

Discarding the negative root, we find:

$$\displaystyle v=600$$

Does this make sense?

#### Wild ownz al

##### Member
AMAZING you are brilliant. Thank you

#### Wild ownz al

##### Member
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

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 $$v+200$$.