SOLUTION: In a trip of 45 km inside and outside a city, a car goes at 50 km / h outside the city and at 30 km / h inside it. If the trip lasts an hour, find out how many kilometers were trav

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Question 1161821: In a trip of 45 km inside and outside a city, a car goes at 50 km / h outside the city and at 30 km / h inside it. If the trip lasts an hour, find out how many kilometers were traveled inside and outside the city.
Found 2 solutions by greenestamps, josgarithmetic:
Answer by greenestamps(13216) About Me  (Show Source):
You can put this solution on YOUR website!


(1) A solution using a traditional formal algebraic method

Let x be the fraction of an hour traveled at 50km/h
Then 1-x is the fraction of an hour traveled at 30km/h

The distances traveled at the two speeds are 50(x) and 30(1-x).

The total distance was 45km:

50%28x%29%2B30%281-x%29+=+45
50x%2B30-30x+=+45
20x+=+15
x+=+15%2F20+=+3%2F4

The car traveled outside the city at 50km/h for 3/4 of an hour, going 50(3/4) = 37.5km; It traveled inside the city at 30km/h for 1/4 hour, going 30(1/4) = 7.5km.

(2) An informal solution method

The average of 45km/h is three-fourths of the way from the city speed of 30km/h to the highway speed of 50km/h.

Therefore 3/4 of the time was spent at the higher speed.

Same answer as before....

Answer by josgarithmetic(39631) About Me  (Show Source):
You can put this solution on YOUR website!
                 SPEED         TIME          DISTANCE
INSIDE            30            1-x           30(1-x)
OUTSIDE           50            x             50x
TOTALS                          1             45

Equation for the total distance, 30%281-x%29%2B50x=45;
Simplify and solve.