Solving a Speed Word Problem Without Quadratics ✈️

There are a lot of lessons to learn from this question, not just distance, speed.

Let me show you in a moment.

A private jet flew from Florida to Seattle.

I like to draw things.

So I think, I think what they're going from east to west and that's going to be a distance of 4200 km before returning along the same route.

Okay, so same distance going and coming back.

4200.

4200.

And they say that the speed for the return trip was 100 km faster than the outbound speed.

So I have over here, return trip was faster.

So if this was a speed of S, this speed is S100.

And they're saying that if the total trip took 13 hours of flying time, what was the jets speed from Florida to Seattle?

So that's Florida to Seattle.

And so this is s, this is S plus 100.

Okay, and if I say that this is time, well the first question is which one took longer?

And it's going to be this, that takes longer.

So if I call this T, this is going to be 13T.

Now I ask myself the following.

Do I really need to create a quadratic equation?

And I might in a moment of panic, but if I slow down and I use some common sense, I realize that there are some numbers that I can plug in.

In if I look at the answer choices, I see a 6, I see a 7, I see a 4200.

And I remember that 6 times 7 equals 42.

And therefore 60 or 6 times 700 is also equal to 4200.

So could I play around with the numbers over here to match this situation described?

And so what I will say is the following.

If I were to have a 700, I'll put it over here, that's a 700.

This means this speed has to have been, should have been a 600.

And then by what do I multiply 600 to get a 4200, that would be seven hours.

Now what I want is this to result in the number that I expect, which is, which has to be 6.

Okay, at 700 it should be 6 hours.

And so if I plug T as 7, will I get also 6?

That will be the correct, situation described.

And so 13 -7 is indeed 6.

So in fact these speeds are as I plugged in, which is six hours on the return flight at 700 kilometers per hour and seven hours on the flight to Seattle at 600 kilometers per hour.

So I did find numbers that match without having to do quadratic equations.

Now what are they asking me for what was the jets speed from Florida to Seattle and that would be 600 kilometers per hour.

So lessons learned.

if you keep things nice and tidy, tidy, you'll have a better chance of noticing certain pairs that you can plug in by looking at the answer choices and then remembering the multiplication table is super valuable.