Question

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?

Answer 1

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

Answer 2

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?

Answer 3

5.143