Question 350906
he is either traveling at 75 mph or 55 mph the whole way.


total time it took for the trip is 1.8 hours.


total distance is 125 miles.


rate * time = distance is the general formula to apply to this type of problem.


let x = the time it takes to travel at 55 miles per hour.


let y = the time it takes to travel at 75 miles per hour.


we get:


55*x + 75*y = 125


55*x is the distance traveled in x hours at 55 miles per hour.


75*y is the distance traveled in y hours at 75 miles per hour.


total distance is 125 miles.


we also get:


x + y = 1.8 since the total time is 1.8 hours.


x is the time it takes to travel at 55 miles per hour.


y is the time it takes to travel at 75 miles per hour.


we solve these 2 equations simultaneously and we get our answer.


from x + y = 1.8 we can solve for y to get y = 1.8 - x


we substitute for y in the equation of:


55*x + 75*y = 125 to get:


55*x + 75*(1.8-x) = 125


Simplify to get:


55*x + 75*1.8 - 75*x = 125


combine like terms and simplify further to get:


-20*x + 135 = 125


subtract 135 from both sides to get:


-20*x = -10


divide both sides by -20 to get:


x = 1/2 = .5


this makes y = 1.8 - .5 = 1.3


looks like .5 hours at 55 mph and 1.3 hours at 75 mph.


55 * .5 + 75 * 1.3 = 27.5 + 97.5 = 125 so the numbers look good.