Algebra word problem

Question

A business executive travels 1120 miles in a corporate jet and the travels an additional 60 miles by car. the plane ride took two hours longer than the car ride. the jet travels 8 times the speed of the the car. find the total time for the 1180 mile trip

Answer 1

Hi James, the best way to solve these problems is to create a table of what is known.

 

Let T be the time for the car ride. Then, T + 2 will be the time for the jet ride.

 

Let S be the speed of the car. Then 8S will be the speed of the jet.

 

Vehicle      Distance        Time      Rate

-------------------------------------------

Airplane       1120           T + 2       8S

 

Car                60                T           S

 

D(istance) = R(ate) * T(ime)

 

Equation for the car:

 

60 = T * S

 

Solve for T:

 

T = 60 / S

 

Equation for airplane:

 

1120 = (T + 2) * 8S

 

Substitute for T:

 

1120 = (60 / S + 2) * 8S

 

Clear the parenthesis:

 

1120 = 480 + 16S

 

Subtract 480 from both sides:

 

16S = 640

 

Divide both sides by 16:

 

S = 40

 

Use the equation for the car to solve for T:

 

60 = T * 40

 

Divide both sides by 40:

 

T = 1.5 hours.

 

Return to the table and enter all information:

 

Vehicle       Distance     Time      Rate
-------------------------------------------
Airplane       1120         3.5         480

Car               60           1.5           40

 

Total time for the full trip: 3.5 + 1.5 = 5 hours.

 

Questions?