The distance between LA and HK is 7,260 mi. It takes the plane 15 hrs to travel, and 12 hrs to come back. Find the speed of plane in air.

Question

Can i see this using two equations?

Answer 1

Distance = Rate times Time, or D = R*T 

 

You don't mention what causes the time difference, but if it is due to a wind with constant speed W then let 

 

S = speed of plane is still air 

 

Then the rate to travel is S - W 

and the rate to come back is S + W 

 

So 

 

7260 = (S - W)*15 = 15*S - 15*W  to travel  

7260 = (S + W)*12 = 12*S + 12*W   to come back

 

Multiply the 1st equation by 4 and the 2nd equation by 5 

 

29040 = 60*S - 60*W

36300 = 60*S + 60*W 

 

Add these 2 equations together 

 

65340 = 120*S

 

S = 544.5 mph is the speed of the the plane in still air 

 

Check:  12*W = 7260 - 12*S by equation 2 so 

            W = (7260 - 6534) / 12 = 60.5 mph 

            S - W = 484 so time to travel is 7260 / 484 = 15 hours

           S + W = 605 so time to come back is 7260 / 605 = 12 hours