Question 1164835: Aaron, Bryan and Collin were waiting to start a race. Collin was 150 m ahead of Bryan and Aaron was 50m behind Bryan. At 8am, they started the race. Aaron over took Bryan in 2min. In another 3 min, Aaron overtook Collin. If Bryan's speed was 120m/min, at what time did Bryan overtake Collin??
Answer by ankor@dixie-net.com(22740)   (Show Source):
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Aaron, Bryan and Collin were waiting to start a race.
Collin was 150 m ahead of Bryan and Aaron was 50m behind Bryan.
:
A------50--------B-------------------150------------------C
:
At 8am, they started the race.
Aaron over took Bryan in 2min.
In another 3 min, Aaron overtook Collin.
If Bryan's speed was 120m/min, at what time did Bryan overtake Collin??
:
a = A's speed in meter/min
b = B's speed = 120 m/min
c = C's speed
:
At 8am, they started the race.
Aaron over took Bryan in 2min.
2a = 2b + 50
2a = 2(120) + 50
2a = 290
a = 290/2
a = 145 m/min is A's speed
In another 3 min, Aaron overtook Collin.
That's a total travel time of 5 min
A travels 200 more meters than C in 5 min
5c + 200 = 5a
Replace a with 145
5c + 200 = 5(145)
5c = 725 - 200
c = 525/5
c = 105 m/min the C's speed
If Bryan's speed was 120m/min, at what time did Bryan overtake Collin??
let t = time in min that B overtakes C
120t = 105t + 150
120t - 105t = 150
15t = 150
t = 150/15
t = 10 min
:
B catch C at 8:10
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