how to write an equation to solve this?

Question

Jim drove to the airport at 30 mph, he then boarded a plane traveling 60 mph. Jim traveled 150 total miles and it took him 3 hours. What is the distance traveled on the plane ride?

Answer 1

Let,

Time Driving = D

Time Flying = F

 

The total time is equal to the sum of driving time and flying time:

 

Total Time = 3 hours = D + F

 

 

Distance is equal to rate (mph) multiplied by the time:

 

Total Distance Traveled = 150 miles = 30 mph * D + 60 mph * F

 

 

Now solve for the system of two equations (and remember units),

 

Equation 1) 3 = D + F

 

    D = 3 - F

 

Equation 2) 150 = 30*D +60*F

    

    Substitute in Equation 1)  150 = 30*(3-F) + 60*F

                                         150 = 90 -30*F + 60*F

                                         150 = 90 + 30*F

                                         40 = 30*F 

     F (flying) = 4/3 hours

 

Substitute F into Equation 1)

 

    D (driving) = 3-(4/3) = 5/3 hours