A British Concorde (BC) and a French Concorde (FC) flew in opposite directions around the earth (40 000 km). The BC covered half of its flight distance at a supersonic speed of 2500 km/h and the other half at a subsonic speed of 1000 km/h. The FC spent half of its flight time at 2500 km/h and the other half at 1000 km/h. Which Concorde completed the trip first, and by how many hours did it beat the other?

BC:

d = rate x time
40,000 = 2500*t
t = 8 hours for the first half.

40,000 = 1000*t
t = 20 hours for the second half.
Total time = 28 hours.

There are ways to go here.
The first is to see if half the time (14 hours) at the FC speeds will come up more or less than 40,000.
d = rt
d = 2500*14 = 35,000 km
d = 1000*14 - 14,000 km
So if FC flies 1/2 the time BC takes FC will cover 49,000 which exceeds the distance which means FC will get there first. Or you can do it mathematically like this.
d1 + d2 = 40,000 km
t1 + t2 = Ttotal
2500(1/2*Ttotal) + 1000(1/2*Ttotal) = 40,000
1250Ttotal + 500Ttotal = 40,000
1750Ttotal = 40,000
Ttotal = 40,000/1750 = a little less than 23 hours.

d1 = rate1 x time1
d2 = rate2 x time2
Add them to obtain
d1 + d2 = 40,000

Mr. Smith is standing 50m from a large bell. With his mighty throwing arm, Mr.Smith throws a rock at the bell and he hears the sound of the bell 4.5s later. If the speed of sound is 330 m/s, what was the speed of the rock in the air?

5.143

Well, buckle up for some high-speed humor and mathematical madness! Let's break it down, shall we?

The BC, being a British Concorde, started with a burst of British enthusiasm, flying at a supersonic speed of 2500 km/h. At this speed, it covered half of its flight distance, which is 40,000 km divided by 2, in no time. And by "no time," I mean it would take roughly 8 hours.

But then, all proper British aircraft need a cup of tea and a little break. So, the BC slowed down to a subsonic speed of 1000 km/h for the remaining half of its journey. At this leisurely pace, it would take another 20 hours to cover the remaining 20,000 km.

Now let's see what our French friend, the FC, was up to. The FC, being a French Concorde, decided to do things the French way. So it flew at 2500 km/h for half of its flight time, covering 20,000 km in about 8 hours.

And here comes the kicker! The FC, like a bon vivant enjoying a leisurely stroll along the Seine, maintained its subsonic speed of 1000 km/h for the other half of its journey. This means it took another 20 hours to cover the remaining 20,000 km.

Crunching the numbers, the BC took a total of 8 hours at supersonic speed and 20 hours at subsonic speed, making it a grand total of 28 hours for the entire trip.

Meanwhile, the FC took the same 8 hours at supersonic speed and the same 20 hours at subsonic speed, also clocking in at a total of 28 hours for the whole shebang.

So, my dear questioner, the British Concorde (BC) and the French Concorde (FC) completed the trip at exactly the same time, in 28 hours! It's a tie! No one came out ahead.

However, in the race of national pride, you could say the British Concorde won by a "hairness" of 2500 km/h, which is the supersonic speed it reached during its journey. But hey, who's keeping score, right?

To find out which Concorde completed the trip first, we need to calculate the total time taken by each Concorde.

Let's start with the British Concorde (BC):

The total distance traveled by BC is 40,000 km. It covered half of its flight distance at a supersonic speed of 2,500 km/h and the other half at a subsonic speed of 1,000 km/h.

So, the time taken for the supersonic portion of the flight by BC is (1/2) * (40,000 km) / (2,500 km/h) = 8 hours.

And the time taken for the subsonic portion of the flight by BC is (1/2) * (40,000 km) / (1,000 km/h) = 20 hours.

Therefore, the total time taken by BC is 8 hours + 20 hours = 28 hours.

Now let's calculate the total time taken by the French Concorde (FC):

Since FC spent half of its flight time at 2,500 km/h and the other half at 1,000 km/h, we need to find the total time it spent flying at each speed.

The total flight time for FC is (40,000 km) / (2,500 km/h) = 16 hours.

Since FC spent half of the time at each speed, it spent 8 hours at 2,500 km/h and 8 hours at 1,000 km/h.

Therefore, the total time taken by FC is 8 hours + 8 hours = 16 hours.

Comparing the total times taken, we find that the British Concorde (BC) completed the trip first, beating the French Concorde (FC) by 12 hours (28 hours - 16 hours).