Question 134600This question is from textbook Algebra Structure and Method
: I have been working on this math problem and I got an answer, but I am not sure if it is right!! I was wondering if someone could help me? I would deeply appreciate it!! Please and Thank you!!
Rate-Time-Distance Problems
Solve.
Jan can run at 7.5m/s and Mary at 8.0m/s. On a race track Jan is given a 25m head start, and the race ends in a tie. How long is the track?
My chart
r * t =d
Jan 7.5 t =7.5t+25
Mary 8.0 t =8.0t
7.5t+25=8.0t
-7.5t -7.5t
25=.5t
divide by .5 and I got 50 then I times that by 8.0 and got 400miles
I don't know if I am right, but I hope someone could help me!!
This question is from textbook Algebra Structure and Method
Found 2 solutions by stanbon, solver91311:
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! Jan can run at 7.5m/s and Mary at 8.0m/s. On a race track Jan is given a 25m head start, and the race ends in a tie. How long is the track?
My chart
r * t =d
Jan: 7.5 t =7.5t+25
Mary 8.0 t =8.0t
7.5t+25=8.0t
-7.5t -7.5t
25=.5t
divide by .5 and I got 50 then I times that by 8.0 and got 400miles
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Jan can run at 7.5m/s and Mary at 8.0m/s. On a race track Jan is given a 25m head start, and the race ends in a tie. How long is the track?
Jan DATA:
rate = 60*7.5 meter/minute ; time = "t+ (25/60)" minutes ; distance = 450(t+(25/60)) = (450t + 187.5) meters
--------------------
Mary DATA:
rate = 60*8 meters/min ; time = t minutes : distance = 480t meters
----------------------
EQUATION:
distance = distance
450t+187.5 = 480t
30t = 187.5
t = 6.25 minutes
-------------------
How long is the track?
distance = 6.25 min * 480 meters/min = 3000 meters or 3 kilometers
=================
Cheers,
Stan H.
Answer by solver91311(24713)  (Show Source):
You can put this solution on YOUR website! You did absolutely everything correctly up until you said 50 times 8.0 is 400 MILES. For that to be true, they would have to be running at speeds of 7.5 and 8.0 MILES per second, that is to say 27,000 miles per hour (Mach 35.5) and 28,800 miles per hour (Mach 40) -- compare to Earth gravity escape velocity of a little over 25,000 miles per hour.
I suspect that the 7.5m/s and 8.0m/s actually mean 7.5 and 8.0 METERS per second, hence 50 seconds time 8.0 meters per second = 400 meters -- once around the track and about par for a human runner.
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