Question 119291
R and A are 30km apart. if they leave at the same time and walk in the same direction, R overtakes A in 60 hours. if they walk towards to each other, they meet in 5 hours. what are their speed?
:
r = R's speed
and
a = A's speed
:
Write a distance equation for each trip, Distance = time * speed:
:
Same direction:
60r - 30 = 60a
60r - 60a = 30
r - s = .5; simplified divided equation by 60
:
Toward each other (total both traveled = 30 km)
5r + 5a = 30
r + a = 6; simplified, divided equation by 5
:
Use these two equation for elimination of a:
r + a = 6
r - a = .5
--------------add
2r +0a = 6.5
r = {{{6.5/2}}}
r = 3.25 km/h is R's speed
:
Use r - a = .5 to find a's speed
3.25 - a = .5
-a = .5 - 3.25
-a = -2.75
a = 2.75 km/h is A's speed
:
:
Check solutions in original equations
60r - 60a = 30
60(3.25) - 60(2.75) =
195 - 165 = 30
and
5r + 5a = 30
5(3.25) + 5(2.75) =
16.25 + 13.75 = 30; confirms our solutions
:
Did this make sense to you? Any questions?