Speed of missile word problem

Question

Two low-flying missiles are launched from the same location at sea and sent in opposite directions. After 10s they are 30,000 ft apart. If one missile travels 500 ft/s faster than the other, what is the speed of this faster missile?

 

 

If you could please provide step by step

 

Thank you!

Answer 1

Let X = speed of slower missile in ft/s

Then X + 500 = speed of faster missile in ft/s  

 

In 10 s the slower missile travels 10*X ft

In 10 s the faster missile travels 10*(X+500) ft 

 

At 10 s they are 30,000 ft apart so 

 

10*X + 10*(X+500) = 30000

10*X + 10*X + 5000 = 30000

20*X = 25000

X = 1250 ft/s is the speed of the slower missile

 

So 1250+500 = 1750 ft/s is the speed of the faster missile

 

Check:  Slower missile travels 10*1250 = 12500 ft in 10 s

            Faster missile travels 10*1750 = 17500 ft in 10 s

            After 10 s they are 12500 + 17500 = 30,000 ft apart