It took a faster runner 10 sec. longer to run a distance of 1500 m than it took a slower runner to run a distance of 1000 m.If the rate of the faster runner was 5 m/sec more than the rate of the slower runner,what was rate of each?
Let V be the speed of the slower runner. Let his (or her) time to run 1000 m be T. The faster runner's speed is V + 5 (in meters per second). Here is what you know:
(V+5)(T+10) = 1500
V*T = 1000
V*T + 5T + 10V + 50 = 1500
5T + 10V = 450
5000/V + 10V = 450 (after substituting 1000 for V*T)
V^2 -45V + 500 = 0
(after multiplying boith sidesw by V and dividing by 10)
(V-25)(V-20) = 0
V = 20 m/s, V+5 = 25 m/s, T = 50s would be one answer
V = 25 m/s, V+5 = 30; T = 40 s would be another answer.
It sounds fishy to me that there are two possible sets of answers. The speeds are also faster than humans can run.
To solve this problem, we can set up a system of equations. Let's call the rate of the slower runner "r" m/sec.
According to the problem, the faster runner took 10 seconds longer to run a distance of 1500 m than the slower runner took to run a distance of 1000 m.
We can use the formula "time = distance / rate" to calculate the time taken by both runners.
For the slower runner:
Time = 1000 / r
For the faster runner:
Time = 1500 / (r + 5) (because the rate of the faster runner is 5 m/sec more than the slower runner)
According to the problem, the faster runner took 10 seconds longer than the slower runner, so we can set up the equation:
1500 / (r + 5) = 1000 / r + 10
Now we can solve this equation to find the value of "r," which represents the rate of the slower runner.
To solve the equation, we can cross-multiply:
1500r = 1000(r + 5) + 10r
Simplifying:
1500r = 1000r + 5000 +10r
Combine like terms:
500r = 5010
Divide both sides by 500:
r = 5010/500
r = 10.02
Therefore, the rate of the slower runner is approximately 10.02 m/sec.
To find the rate of the faster runner, we can use the formula "rate = r + 5" since the rate of the faster runner is 5 m/sec more than the slower runner.
Substituting the value of "r" in the equation, we get:
Rate = 10.02 + 5
Rate = 15.02
Therefore, the rate of the faster runner is approximately 15.02 m/sec.
In summary, the rate of the slower runner is approximately 10.02 m/sec, and the rate of the faster runner is approximately 15.02 m/sec.