Question 951840

Bob drove {{{d[1]=200mil}}}  in the same amount of time {{{t}}} that it took a propeller plane to fly {{{d[2]=1100mil}}}

{{{d[1]=200mil}}} in time {{{t}} is:

{{{d[1]=s*t}}}

{{{speed =s (mil/h)}}}

a propeller plane to fly:
 
{{{d[2]=1100mil}}} in same time {{{t}}}:

{{{d[2]=s*t}}}

since given that the speed of the plane was {{{180(mil/h)}}} greater then speed of a car, we have 

{{{speed =(s +180)(mil/h)}}}

now we have for the car:

{{{200mil=s(mil/h)*t}}}

and the plane:

{{{1100mil=(s +180)(mil/h)*t}}}

since given that {{{t}}} equal, we have

{{{t=200mil/s(mil/h)}}}....the car
and
{{{t=1100mil/(s +180(mil/h))}}}.......the plane

so,  
{{{200mil/s(mil/h)=1100mil/(s(mil/h) +180(mil/h))}}} ...simplify


{{{2/s=11/(s +180(mil/h))}}}

{{{2(s +180(mil/h))=11s}}}

{{{2s +360(mil/h)=11s}}}

{{{360(mil/h)=11s-2s}}}

{{{360(mil/h)=9s}}}

{{{s=360(mil/h)/9}}}

{{{s=highlight(40(mil/h))}}}.....the speed of {{{car}}} 

{{{s +180(mil/h)=40(mil/h) +180(mil/h)=highlight(220(mil/h))}}}.....the speed of {{{plane}}} 

check:

car
{{{t=200mil/s}}}

{{{t=200mil/40(mil/h)}}}

{{{t=5h}}}

plain

{{{t=1100mil/(s +180(mil/h))}}}
{{{t=1100mil/(220(mil/h))}}}
{{{t=5h}}}

so, the time is same 

your answer is:

the speed of {{{car}}} is {{{highlight(40(mil/h))}}} and the speed of {{{plane}}}  is {{{highlight(220(mil/h))}}}