Question 1208292
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Jada is calling from a city 65 miles away and wants to meet Destiny somewhere between 
the two locations. Jada says she will start driving right away, but Destiny needs 10 mins 
to finish her lunch before she can begin driving. Jada plans to drive at 65 mph, 
whereas Destiny usually averages about 75 mph. ignore acceleration and assume the highway 
is a straight line. 
(a) How many minutes t{{{highlight(cross(meet))}}} will Jada be driving before she meets Destiny?
(b) how many miles d will Destiny have traveled when they meet.
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<pre>
Jada is driving t minutes at the rate {{{65/60}}} miles per minute.

Destiny is driving (t-10) minutes at the rate {{{(75/60)}}} miles per minute, from the problem.


The distance Jada will cover is  {{{(65/60)*t}}} miles.

The distance Destiny will cover is  {{{(75/60)*t}}} miles.


The two partial distances comprise the total distance of 65 miles.


So, the total distance equation is

    {{{(65/60)t}}} + {{{(75/60)*(t-10)}}} = 65  miles.


Multiply both sides by 60

    65t + 75(t-10) = 65*60.


Simplify and find t, in minutes

    65t + 75t - 750 = 4550

        140t        = 3900 + 750

        140t        =    4650

           t        =    46500/140 = 33.21428571 minutes.


 The driving time for Jada is 33.21428571 minutes.   It is the <U>ANSWER</U> to question (a).


Destiny will travel  33.21428571-10 = 23.21428571 minutes.


Destiny will travel  {{{23.21428571*(75/60)}}} = 29.01785714 miles.  It is the <U>ANSWER</U> to question (b).


<U>CHECK</U>.  The total traveled distance is  {{{33.21428571*(65/60) + 29.01785714}}} = 65 miles, total distance.  ! correct !
</pre>

Solved.


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The numbers are slightly idiotic - but it is because the input numbers are given this way.


The rest is correct.  You can make rounding everywhere, where you want.