Q:

Devon and Michael ran a 5-mile race. Devon ran 2 miles per hour faster than Michael and finished the race 5 minutes before Michael did. If x represents Michael's speed (in miles per hour), which equation could represent this situation? Answer Choices 5x+2−5x=112 5x−5x+2=112 x+25−x5=112 x+25+x5=112 Part 2 What was Michael's speed? miles per hour

Accepted Solution

A:
let
x------------> Michael's speed  (in miles per hour)
y------------> Devon's speed  (in miles per hour)

we know that
y=x+2-------> equation 1
speed=distance/time--------> time=distance/speed
distance =5 miles
Michael's time=5/x
Devon's time=5/y
the difference [Michael's time-Devon's time]= 5 minutes

1 hour--------> 60 min
x-------------> 5 min
x=5/60 hour

5/x-5/y=5/60-----------> multiply by 60 both members
300/x-300/y=5-------> (300/x)-5=300/y-------> (300-5x)/x=300/y
y/300=x/(300-5x)------> y=300x/(300-5x)-----> y=60x/(60-x)-----> equation 2

equation 1 =equation 2
x+2=60x/(60-x)--------> (60-x)*(x+2)=60x------> 60x+120-x²-2x=60x
x²+2x-120=0
  
 using a graph tool ----->to resolve the second order equation
the solution is 
x=10
then
Michael's speed is 10 miles/hour
Devon's speed is 10+2-----> 12 miles/hour