SOLUTION: A driver makes a 125 mile trip from Phoenix to Tucson with the cruise control set at either 55 mph or 75 mph the whole way. If the trip took 1.8 hours, how long did the driver trav

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Question 350906: A driver makes a 125 mile trip from Phoenix to Tucson with the cruise control set at either 55 mph or 75 mph the whole way. If the trip took 1.8 hours, how long did the driver travel at 55 mph?
if i had an equation to solve this problem, i can solve similar problems. I was thinking along the lines of 55x+ 75y= 1.8?? iknow it has something to do with the slope formula....but i dont know how. Ive been working on this and similar problems for over an hour, and cant seem to figure how to solve it.
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
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.