Two planes left the same airport traveling in opposite directions.

Question

Enter an equation that can be used to solve this problem, where x represents the number of hours that the first plane had been traveling.

Two planes left the same airport traveling in opposite directions. The first plane left the airport at 2 P.M. traveling at an average rate of 500 mph. The second plane left the airport at 4 P.M. traveling at an average rate of 550 mph. When will the planes be 3100 miles apart?

Enter the amount hours, after the first plane left, when the planes will be 3100 miles apart.

Answer 1

Hello Sade,

 

Your problem is an example of a distance problem, so you muct know the formula to find the distance. To find the distance we simply multiply the rate by the time, or you'll see more often , d = r t. That means to calculate distance traveled you need rate and time.

 

Your problem states that there are 2 planes, leaving the same airport,  2 hrs apart and travelling in opposite directions.

 

They are looking for the number of hours the first plane has traveled when the planes will be 3,100 miles apart.

 

 

Take note, planes are traveling in opposite direction, which means 3100 miles will be the sum of the distances that the two planes have traveled.

 

D (Plane 1) + D(Plane 2). = 3100

 

To find the distance traveled of plane 1 we need to find the rate and time traveled of plane 1. Rate is 500mph and time , we don't know, let us use x.

rate = 500

time = x

D (plane1) = 500x

 

For plane 2, rate is 550 mph and time is 2 hrs less than the time of plane 1 , so that is equal to  x - 2  ( plane 1 left 2 hrs earlier so it would have traveled 2 more hours than plane 2)

rate = 550 mph

time =( x-2 ) hours

D(plane2) =  550(x -2)

 

now that we have all the information we need, we can plug these into our equation to solve for x, the number of hours traveled by plane 1

 

D(plane1) + D(plane2). = 3100

500x  +  550(x- 2) =  3100

500x + 550x -  1100 = 3100

1050x - 1100 =   3100

          +1100   + 1100

           ---------  --------

1050x   =  4200

--------     ------

1050        1050

 

x = 4 hrs.

 

4 hrs after the first plane left , plane 1 and plane 2 wold be 3100 miles apart.

 

Check:

D( plane1) + D(plane2)  ?=. 3100

500*4  +  550*2   ?=  3100

2000 + 1100  ?=  3100

              3100 = 3100

 

Good luck and hope it helps!