SOLUTION: Jan can run at 7.5 m/s and Mary at 8.0 m/s. On a race track Jan is given a 25 m head start, and the race ends in a tie. How long is the track?

Question 57404This question is from textbook Algebra: Structure and Method
: Jan can run at 7.5 m/s and Mary at 8.0 m/s. On a race track Jan is given a 25 m head start, and the race ends in a tie. How long is the track? This question is from textbook Algebra: Structure and Method

Found 2 solutions by Paul, funmath:
Answer by Paul(988) (Show Source): You can put this solution on YOUR website!
Let x represent the length of the track
EQUATION:
7.5x+25=8x
0.5x=25
x=50
Hence, the track is 50m long.
Paul.
Answer by funmath(2933) (Show Source): You can put this solution on YOUR website!
Jan can run at 7.5 m/s and Mary at 8.0 m/s. On a race track Jan is given a 25 m head start, and the race ends in a tie. How long is the track?
The formula for distance: , where d=distance, r=rate, and t=time.
They ran the same amount of time:t
The race is the same distance for both: d
The distance Jan went is:d= 7.5t+25
The distance Mary went is: d= 8.0t
The equation to solve for time is is:
7.5t+25=8.0t
-7.5t+7.5t+25=-7.5t+8.0t
25=.5t
25/.5=.5t/.5
50=t
t=50 s
We were asked how long the race was, so plug t=50 s into Mary's distance equation:d= 8.0t
d=8.0(50) m
d=400 m
Happy Calculating!!!
RELATED QUESTIONS
Please help me solve the word problem: Jan can run at 7.5 m/s and Mary at 8.0 m/s. On a... (answered by rfer,MathTherapy)
Jan can run 7.5 meters per second, Mary at 8.0 meters per second. On a race track Jan is... (answered by mananth,corncob)
I have been working on this math problem and I got an answer, but I am not sure if it is... (answered by stanbon,solver91311)
In a 75 m race if ace gives flash a 15 m head start, ace and flash will tie. If flash... (answered by ankor@dixie-net.com)
There is a circular track of 440 meters. There are three persons Symonds, Harbhajan and... (answered by ankor@dixie-net.com)
In a 500 m race, Ravi beats Ramesh by 5 seconds or 100 m. They decide to run another race (answered by y6n3o9p4)
A cyclist has a head start of 75 m in a race and is moving with constant speed of 10m/s.... (answered by Fombitz)
A speedy tortoise can run at 0.15 m/s, and a hare can run 16 times as fast. In a race,... (answered by Boreal)
1. In a swimming race, a father gives his 4-year old son a 10-second head-start. The pool (answered by ankor@dixie-net.com)