Creating Rational Functions Question

Question

Here is our scenario: 

“A ‘leaf-peeper’ drives 90 miles along a scenic highway through a forest mixed with maples, oaks and birch, to admire the fall foliage. The colors are amazing, and it is difficult to keep their eyes on the road. At the end of the scenic highway the leaf-peeper turns around and drives back the same way. This time, despite the new perspective, they’ve seen much of the sights, their focus on the road is better and they drive at an average 10 miles per hour faster than the outgoing journey.” 

Resource: 

         

Express the total time required to complete the round trip as a function of the average velocity of the outgoing trip. 

Answer 1

Main Equation: D = RT

Distance = Rate * time

Outgoing Trip (#1)

D1 = (R1)(T1)

90 = (R1)(T1)

T1 = 90/(R1)

Return Trip (#2)

D2 = (R2)(T2)

90 = (R1 + 10)(T2)

T2 = 90/(R1 + 10)

Total Time = T1 + T2

Total Time = 90/(R1) + 90/(R1 + 10)