Question 166370
miles per hour(speed)=distance/time
{{{m/h=d/t}}}
equation 1 {{{m/h=(30miles)/((t)hours)}}}
equation 2 {{{m/h=(50miles)/((t)hours+8(minutes))}}}
set the equations = to each other
{{{(30miles)/((t)hours)=(50miles)/((t)hours+8(minutes))}}}
convert the 8 minutes to hours.  8(minutes)=8/60 hours which reduces to 2/15 hours.
so now you have the equation:
{{{(30miles)/((t)hours)=(50miles)/((t+2/15)hours)}}}
Solve for t:
cross multiply and get
{{{30(t+2/15)=50(t)}}}
{{{30t+60/15=50t}}}
subtract 30t from each side
60/15=20t
multiply each side by 15
60=300t
divide each side by 300
{{{1/5=t}}}
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we remember that t=time in hours and we are trying to find speed. so we plug t into either speed formula to find our speed.  
First formula:  equation 1 {{{m/h=(30miles)/((1/5)hours)}}}
Second formula: equation 2 {{{m/h=(50miles)/((1/5)hours+(2/15)(hours))}}}
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Answer:  Top speed is {{{150}}}{{{miles}}}/{{{hour}}}
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