Question 985002
<i>An automobile can travel D kilometers in the same time t that a truck can travel d kilometers.
If an automobile travels at a speed of p kph faster than the truck,
what is the speed of the automobile?</i>


R, car speed
r, truck speed
R=r+p


VARIABLES ASSIGNED
{{{system(D=200,d=150,p=15)}}}


VARIABLES UNKNOWN
t, time of each vehicle
R and r

<pre>
         speed   time    distance
CAR       r+p       t       D
TRUCK     r         t       d

</pre>


The question means, what is R?


The tabulated data gives this system:
{{{highlight(system((r+p)*t=D,rt=d))}}}


Solve the system for r and t.  This will require a few algebraic steps.  Use the value result
of r to evaluate R.


{{{rt+pt=D}}}
{{{d+pt=D}}}
{{{pt=D-d}}}
{{{t=(D-d)/p}}}


Substitute for t in either equation, the "d" equation being arbitrary choice here.
{{{r((D-d)/p)=d}}}
{{{highlight(r=dp/(D-d))}}}------substitute the values given and evaluate r, and then use this
to evaluate R.