One plane leaves the airport and travels west at 490 mph. a second plane leaves 2 hours later and travels north at 540 mph. at what rate is the distance between the two planes changing at when the second plane has been traveling for 3 hours

The rate at which both the plane changing distance is 522 mph

Step-by-step explanation:

Given as :

The west going plane travel distance (Dw) = 490 mile

The west going plane leave airport time at (Tw) = T  hour

The north going plane travel distance (Dn) = 540 mile

The north going plane leave airport time at (Tn) = ( T + 2 )  hour

Let the Rate at which second plane changes distance = S  mph

As per question the north going plane travel fro 3 hours

So, Speed of north going plane (Sn) =

Or,                                                 Sn =  

Or,                                                 Sn =

∴                                                   Sn = 180 mph

Now ,∵ North going plane travel for 3 hours so,

                          Tn = 3 h

Or,                      T + 2 = 3 h

So,                        T = 3 - 2 = 1 h

∴ The time cover by west gong plane = 1 h

So, Speed of west going plane (Sw) =

Or,                                                 Sw =  

Or,                                                 Sw =

∴                                                    Sw = 490 mph

So, The rate at which both plane changing =  

Or,  The rate at which both plane changing =

∴     The rate at which both plane changing = 522 mph

Hence The rate at which both the plane changing distance is 522 mph Answer  

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explanation:

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