Question

1. Lyft Rates Lyft charges customers a flat fee per ride (which is
higher during rush hour traffic) plus charges for each minute
and each mile. (Data from: www.lyft.com.) Suppose that, in a
certain metropolitan area during rush hour, the flat fee is $4,
the cost per minute is $.20, and the cost per mile is $1.40. Let x
be the number of minutes and y the number of miles. At the
end of a ride, the driver said that you owed S14 and remarked
that the number of minutes was three times the number of
miles. Find the number of minutes and the number of miles for
this trip.

Answer 1

The total price is

$4+0.2x+1.40y$

where x is the number of minutes and y is the number of miles.

We know that the number of minutes was three times the number of

miles, i.e. x=3y. This changes our expression into

$4+0.2\cdot 3y+1.40y=4+0.6y+1.40y=4+1.46y$

We also know that the total cost was 14, so we have

$14=4+1.46y\iff 1.46y=10 \iff y=\dfrac{10}{1.46}\approx 6.85$

And since the number of minutes was three times the number of miles, it is

$3\cdot 6.85=20.55$