SOLUTION: Autumn can run 70 yards in 14 seconds. Chasity can run the same distance in 16 seconds. If Chasity is 30 yards ahead of Autumn when they both start running, how long does it take f

Question 1096096: Autumn can run 70 yards in 14 seconds. Chasity can run the same distance in 16 seconds. If Chasity is 30 yards ahead of Autumn when they both start running, how long does it take for Autumn to catch Chasity?
a) How long does it take for Autumn to catch Chasity? (in Seconds)
b) How many yards does Autumn have to run to catch Chasity?(in Yards)
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
Autumn runs 5 yards per second (70/14)
Chasity runs 70/16=4.375 yards per second.
Autumn is catching up at 0.625 yards per second (5-4.375)
She is 30 yards behind Chasity. 30/0.625= 48 seconds.In that time, she will run 240 yards.
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distance=velocity* time
When A catches C, she will have run 30 yards further,since she starts off behind and they will meet.
For A
x+30=5*t, where the units are yards on the left and seconds*yards/seconds on the right.
For C
x=4.375*t, because they both run for the same length of time
x=5t-30
x=4.375 t
Set the two equal to each other, since they are both equal to x
5t-30=4.375t
0.625t=30
t=48 seconds
Autumn runs 5 yards/second, so that is 240 yards.
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