Question

There are two shipping options available: Land and Air. All three can be shipped simultaneously regardless of travel option chosen.
Travel speeds are as follows:
Land: vLand = 50t
Air: vAir = 200t

where t is time in seconds. Also, sLand = 0 and sAir = 0 at t = 0, if sLand and sAir are the distances traveled at time t by the two possible means of transportation.

It takes 200 seconds to ship all three from A to B by land. How long does it take by air?

Answer 1

It takes 50 seconds.

We will use the formula d = rt for this, where d is the distance traveled, r is the speed and t is the amount of time.

For land travel,
d = 50t

Since it takes 200 seconds by land, this gives us
d = 50(200) = 10,000

Now we use this same distance in the formula for air travel:
d = 200t
10,000 = 200t

Divide both sides by 200:
10,000/200 = 200t/200
50 = t