Question

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?

Answer 1

2 km
Change 54 minutes to hours:
`(54)/(60) = (9)/(10)` hours
Let t = time it takes to get to his friend's house
Thus
`(9)/(10) -t` = time it takes to return home
Distance to Friend's house = Distance back home

`4t=5( (9)/(10) -t)` distance = speed x time

`4t= (9)/(2) -5t` distributive property

`9t= (9)/(2)` add 5t to both sides of the equation

`t= (1)/(2)` divide both sides by 9
To find the distance to the friend's house 4 x 1/2 = 2 km