A British Concorde and a French Concorde leave, going in the same direction

[TNewC]

Homework Statement

Both Concords are going 40 000 km.
The British Concorde spends half its DISTANCE at 2500 km/hr, and the other half at 1000 km/hr. The French Concorde spends half it's TIME at 2500 km/hr, and the other half at 1000 km/ hr. Which one arrived at their destination first?

Homework Equations

d=vt

The Attempt at a Solution

I can do the calculations for the British Concorde, to find time, but I can't quite figure out how to do the calculations for the French Concorde. Please help? The only thing I can think of is this:
1/2t=40 000km/2500 km/hr for the first half of the time
Which is 16 hours, and then:
1/2t=40 000 km/1000 km/hr
Which is 40 hours

What I can't figure out, is whether to divide them both by 1/2 then add, or just add them together. Help?

 

[Galadirith]

Hi TNewC,

Well I think actually you have approached the way of solving for the French Concorde slightly wrong. So let's think through the step by step, the combined distance traveled by the French Concorde (FC) at both speeds equals 40,000 km, which is what you didn't do in your attempt, you can't consider the distances traveled at different speeds separately.

So let us say that the distance traveled at 2500 km/hr is D₁ and the distance traveled at 1000 km/hr is D₂. So we have:

$$40000 = D_1 + D_2$$

But can express D₁ and D₂ in another way as shown by the equation you put:

$$40000 = 2500\left(\frac{t_t}{2}\right) + 1000\left(\frac{t_t}{2}\right)$$

There hopefully you can see I have replaced D₁ and D₂ with vt, where v is their respective speeds and t = t_t/2 because they spend half the total time at these speeds. Note that I have written t_t, meaning total time, instead of just t, to distinguish between the variable t in the equation d = vt and the time for this problem.

Now ill leave you there, hopefully you can see now it simply boils down to solving this simple equation for t :D, have fun TNewC

 

[TNewC]

Thank you so much Galadirith! I really appreciate your answer, and you've managed to explain it all quite clearly. I actually understand it now :D