A sparrow flies to see a friend at a speed of 4km/h. His friend is out, so the sparrow immediately returns home at a speed of 5km/h. The complete journey took 54 minutes. How far away does his friend live?
2 km Change 54 minutes to hours: [tex] \frac{54}{60} = \frac{9}{10} [/tex] hours Let t = time it takes to get to his friend's house Thus [tex] \frac{9}{10} -t[/tex] = time it takes to return home Distance to Friend's house = Distance back home [tex]4t=5( \frac{9}{10} -t)[/tex] distance = speed x time [tex]4t= \frac{9}{2} -5t[/tex] distributive property [tex]9t= \frac{9}{2} [/tex] add 5t to both sides of the equation [tex]t= \frac{1}{2} [/tex] divide both sides by 9 To find the distance to the friend's house 4 x 1/2 = 2 km
