Question

Two planes, which are 3400 miles apart, fly toward each other. Their speeds differ by 80mph. If they pass each other in 5 hours, what is the speed of each?

Answer 1

Answer : The speed of both planes is 61.25 mph and 18.75 mph  respectively.

Explanation:

Let the speed of first plane be x mph

Let the speed of second plane be y mph

Since we have given that difference of speeds is 80 mph

i.e.  x - y= 80   ($Eq^n$   1)

Distance between two planes = 3400 miles

As they are flying towards each other i.e. they are in the opposite direction.

So, Relative speed  will  be the sum of their speeds i.e.

Relative speed = x + y

And we know speed = $\frac{Distance}{Time}$

Speed= $\frac{3400}{80}$

⇒ Speed = 42.5 mph

Hence, Relative speed becomes 42.5 mph

⇒ x+y=42.5  ($Eq^n$   2)

Now, by using the elimination method of solving the system of equation, we  have ,

x= 61.25 mph

and y = 18.75 mph