SOLUTION: A family drove to Las Vegas at an average speed of 65mph and returned via the same route at a speed of 70mph. Find the time it took to drive to Las Vegas if the total time was 27 h

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Question 808700: A family drove to Las Vegas at an average speed of 65mph and returned via the same route at a speed of 70mph. Find the time it took to drive to Las Vegas if the total time was 27 hours.
Answer by josgarithmetic(39614) About Me  (Show Source):
You can put this solution on YOUR website!
_________speed__________________time_________________distance
_________65_____________________x____________________65x
_________70_____________________y____________________70y
Total___________________________27___________________65x+70y


You want one variable, not two.
x+y=27 so maybe, y=27-x. Try this instead of "y".

_________speed__________________time____________________distance
_________65_____________________x_______________________65x
_________70_____________________27-x____________________70(27-x)
Total___________________________27______________________65x+70(27-x)

The given information still does not seem enough.
Note, the distance both ways is the same, as described.


Let this distance be d.
highlight%2865x=70%2827-x%29%29
Solve for x and you can compute distance for either direction.

65x=70%2A27-70x
65x%2B70x=70%2A27
Divide b.s. by 5,
13x%2B14x=14%2A27
27x=14%2A27
highlight%28x=14%29

That much could well have been done using two variables, x and y and we would have had a system of two equations.

Use either distance expression with x=14 and find the distance:
65%2Ax=65%2A14=highlight%28910%29 miles