SOLUTION: Hi a b c were waiting to start a race.c was 150m ahead of b and a was 50m behind b. At 8am they started the race.a overtook b in 2 min.in another 3 min a overtook c. If b speed w

Question 1105697: Hi
a b c were waiting to start a race.c was 150m ahead of b and a was 50m behind b. At 8am they started the race.a overtook b in 2 min.in another 3 min a overtook c. If b speed was 120m/min at what time did b overtake c, assume they all ran at a constant speed throughout the race.
thanks

Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
a b c were waiting to start a race.
c was 150m ahead of b and
a was 50m behind b.
At 8am they started the race.
a overtook b in 2 min.in another 3 min a overtook c.
If b speed was 120m/min at what time did b overtake c?
:
Find a's speed
In 2 min b traveled 240m
a traveled 240 + 50 = 290m in 2 min, therefore
290/2 = 145 m/min is a's speed
:
Find c's speed
At start c was 200m ahead of a
It took a, 5 min to overtake c
in 5 min a travels 5(145) = 725m
c traveled 725 - 200 = 525m, therefore
525/5 = 105 m/sec is c's speed
:
"If b speed was 120m/min at what time did b overtake c?"
b was 150m behind c
let t = time for b to catch c, write a dist equation (dist = speed * time)
120t = 105t + 150
120t - 105t = 150
15t = 150
t = 150/15
t = 10 min
b catches c at 8:10

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