When going to the beach, Guilherme takes 2 hours on the road to go from his city to the beach and 3 hours to get back to his city. Knowing that Guilherme's car goes at 100 km/h when downhill, 80 km/h on plane surfaces and 60 km/h uphill, and that there are only 8 kilometers of road on plane surface, what is the distance in kilometers between the city and the beach?
+128406 Time spent on plane surface = 8km / 80km/h = (1/10) h
Distance / rate = time
Let x be the downhill part and y be the uphill part from the city to the beach
Then...on the return trip, the roles are reversed.....y is the downhill part and x the uphill part
So we have this system of total times ( in hrs)
x / 100 + y/ 60 + 1/10 = 2
y/100 + x / 60 + 1/10 = 3 simplify
x/100 + y/60 = 1.9
y/100 + x/60 = 2.9 mutiply both equations through by 300.....arrange as:
3x + 5y = 570 ⇒ mult through by 5 ⇒ 15x + 25 y = 2850
5x + 3y = 870 ⇒ mult through by -3 ⇒ -15x - 9y = -2610 add these
16y = 240
y = 15 (km)
3x + 5(15) = 570
3x + 75 = 570
3x = 495
x = 165 (km)
Total distance = 165 + 15 + 8 = 188 km
+373 Hey there, Guest!
So...
Travelling at 8 Km at 80 km/hr takes 1/10 hours while travelling at \(X\) km at 100 km/hr takes \(\frac{x}{100}\) hours, and travelling at \(Y\) km at 60 km/hr takes \(\frac{y}{60}\) hours; in one direction, the sum of these is 2 hours, so \(\frac{1}{10}\) + \(\frac{x}{100}\) + \(\frac{y}{60}\) = 2. In the other direction, however, whatever was uphill becomes downhill, etc.; so the roles of x and y change, and we get the equation:
1/10 + x/60 +y/100 =3.
That equation can be simplified to get:
6x + 10y = 1140
&
6y + 10x = 1740
Therefore the answer is x=165 km, and y = 15 km.
So the total distance is 165 + 15 + 8 = 188 km.
Hope this helped! :)
( ﾟдﾟ)つ Bye
