Determining the Cheaper Option: Airport Taxi vs. Limousine

  • Thread starter Thread starter Ericca
  • Start date Start date
AI Thread Summary
The discussion centers on comparing costs between an airport taxi and a limousine service for client pickup. The taxi charges $6.00 plus $0.50 per kilometer, while the limousine has a flat rate of $40. To determine when the costs are equal, the equations L = 40 for the limousine and T = 6 + 0.50x for the taxi can be set equal to each other. Solving this system reveals the distance at which both options cost the same, indicating that below this distance, the taxi is cheaper, and beyond it, the limousine is more economical. This analysis helps Darrell decide the most cost-effective transportation option based on the distance to the destination.
Ericca
Messages
3
Reaction score
0
Darrell is making arrangements to pick up a client at the airport. Airport taxi charges $6.00, plus $0.50 per kilometre. Airport limo charges a flat rate of $40 for its limousine service.
a)Write a system of equations that describes the cost of the taxi and limoousine.
b)solve the system you wrote in a
c) Explain what the solution to the system represents.
d) Darrell is trying to decide whether the taxi or the limo is cheaper. What advice would you give Darrell?
 
Mathematics news on Phys.org
Shouldn't this be in the homework section? (And shouldn't you show us what you have already done?)

The equation for the limousine is easy! Letting L be the cost of the limosine and x the distance driven: L= 40, of course.
The equation for the taxi is almost as easy: Letting T be the cost of the taxi and x the distance driven: T= 6+ 0.50x.

b) I have no idea what you mean by "solve the system you wrote in a". In the first place, it's not really a system- it's two separate equations. In the second, what do you want to solve for?

c) Uh, yeah, that's what I'd like you to do!

d) Okay, I suspect that the problem wants you to set L= T in the two equations and solve for x: the distance at which the two costs are the same. Below that distance, the taxi is cheaper, beyond, the limousine is cheaper.
 

Thread 'What Exactly is Dirac’s Delta Function? - Insight'

Insights auto threads is broken atm, so I'm manually creating these for new Insight articles. In Dirac’s Principles of Quantum Mechanics published in 1930 he introduced a “convenient notation” he referred to as a “delta function” which he treated as a continuum analog to the discrete Kronecker delta. The Kronecker delta is simply the indexed components of the identity operator in matrix algebra Source: https://www.physicsforums.com/insights/what-exactly-is-diracs-delta-function/ by...
View full post »

Thread 'Fermat's Last Theorem'

Fermat's Last Theorem has long been one of the most famous mathematical problems, and is now one of the most famous theorems. It simply states that the equation $$ a^n+b^n=c^n $$ has no solutions with positive integers if ##n>2.## It was named after Pierre de Fermat (1607-1665). The problem itself stems from the book Arithmetica by Diophantus of Alexandria. It gained popularity because Fermat noted in his copy "Cubum autem in duos cubos, aut quadratoquadratum in duos quadratoquadratos, et...
View full post »
Thread 'Imaginary Pythagorus'

Thread 'Imaginary Pythagorus'

I posted this in the Lame Math thread, but it's got me thinking. Is there any validity to this? Or is it really just a mathematical trick? Naively, I see that i2 + plus 12 does equal zero2. But does this have a meaning? I know one can treat the imaginary number line as just another axis like the reals, but does that mean this does represent a triangle in the complex plane with a hypotenuse of length zero? Ibix offered a rendering of the diagram using what I assume is matrix* notation...
View full post »

Similar threads

Prestigious Private School vs Honors at State Flagship
Replies
7
Views
3K

Hot Threads

Recent Insights

Back
Top