SOLUTION: Two contestants run a 440-yard course. The first wins by 4 seconds when given a head start of 200 feet. They finish together when the first is given a head start of 40 yards. Find
Algebra.Com
Question 638443: Two contestants run a 440-yard course. The first wins by 4 seconds when given a head start of 200 feet. They finish together when the first is given a head start of 40 yards. Find the speed of each in feet per second.
I tried to solve by using the formula D (distance)= s (speed) x t (time).
But I come up with two equations for each situation. Converting yards to feet: 440yards=1320 feet:
runner #1: s(t-4)=1120 (wins by 4 seconds)
runner #2: s(t)=1320
and for the second situation:
runner #1: s(t)=1200 (given a 40 yard=120feet head start: 1320-120=1200 feet).
runner #2 s(t)=1320
then solving for s: s=1320/t and substituting 1320/t(t-4)=1120 and solving for t, 1320t-5280=1120t, t=26.4 secs, then s=1320/t and s=1320/26.4= 50ft/sec.
Now, obviously a human cannot run at that speed, so this does not seem like a plausible answer, and I cannot figure out why I have four equations, I also tried to use different combinations but this didn't work either. So, I trust someone with better mathematical acumen can come up with a better solution. Thank you so kindly for trying to solve this problem. I look forward to the correct solution and appreciate your time and assistance.
Answer by MathTherapy(10551) (Show Source): You can put this solution on YOUR website!
Two contestants run a 440-yard course. The first wins by 4 seconds when given a head start of 200 feet. They finish together when the first is given a head start of 40 yards. Find the speed of each in feet per second.
I tried to solve by using the formula D (distance)= s (speed) x t (time).
But I come up with two equations for each situation. Converting yards to feet: 440yards=1320 feet:
runner #1: s(t-4)=1120 (wins by 4 seconds)
runner #2: s(t)=1320
and for the second situation:
runner #1: s(t)=1200 (given a 40 yard=120feet head start: 1320-120=1200 feet).
runner #2 s(t)=1320
then solving for s: s=1320/t and substituting 1320/t(t-4)=1120 and solving for t, 1320t-5280=1120t, t=26.4 secs, then s=1320/t and s=1320/26.4= 50ft/sec.
Now, obviously a human cannot run at that speed, so this does not seem like a plausible answer, and I cannot figure out why I have four equations, I also tried to use different combinations but this didn't work either. So, I trust someone with better mathematical acumen can come up with a better solution. Thank you so kindly for trying to solve this problem. I look forward to the correct solution and appreciate your time and assistance.
Let the speed of the 1st runner be , and speed of 2nd,
The course is 440 yards, or 1,320 feet
Since the 1st gets a headstart of 200 feet, then the 1st travels 1,320 – 200, or 1,120 feet
Time taken by 1st to go 1,120 feet, plus time won by, equals time taken by 2nd to go 1,320 ft, OR
---- Multiplying by LCD, ---- eq (i)
Since the 1st gets a headstart of 40 yards, or 120 feet, then the 1st travels 1,320 – 120, or 1,200 feet
Time taken by 1st to go 1,200 feet equals time taken by 2nd to go 1,320 ft, OR
---- Cross-multiplying ---- eq (ii)
Therefore, ---- ----- Substituting for in eq (i)
----- Factoring out GCF, 4
---- Factoring out GCF,
, or speed of 1st runner = ft/s
---- Substituting 20 for in eq (ii)
, or speed of 2nd runner = , or ft/s
You can do the check!!
Send comments and “thank-yous” to “D” at MathMadEzy@aol.com
RELATED QUESTIONS
In a 500 m race, Ravi beats Ramesh by 5 seconds or 100 m. They decide to run another race (answered by y6n3o9p4)
Dick can run the 440 yard dash in 55 seconds, and Jack can run it in 88 seconds. How... (answered by CharlesG2)
Dick can run the 440 yard dash in 55 seconds, and Jack can run it in 88 seconds. How... (answered by macston)
Contestants in a long distance race run 5 kilometers due south. The runners then turn... (answered by chen.aavaz)
it takes Pedro 60 seconds to run around a 440 yard track . how long does it take Juan to... (answered by ankor@dixie-net.com)
It takes Michael 60 seconds to run around a 440-yard track. How long does it take Jordan... (answered by macston)
mr. and mrs. austria love to run around the town. from past experiences, they know that... (answered by Alan3354)
Mr. and Mrs. Austria love to run around the town. From past experiences, they know that... (answered by JBnovelwriter,greenestamps,ikleyn)
Alex is a faster runner than Bob. Alex runs 3 yards every second. Bob runs 2.5 yards... (answered by ankor@dixie-net.com)