Posted by **jack** on Monday, August 23, 2010 at 4:15am.

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?

- math -
**drwls**, Monday, August 23, 2010 at 5:29am
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.

## Answer this Question

## Related Questions

- algebra - If one runner can run 10 meters in one second and another runner can ...
- algebra - Two persons are to run a race, but one can run 8 meters per second, ...
- algebra - Two persons are to run a race, but one can run 10 meters per second, ...
- Physics - Runner A is running at a constant rate of 2.3 m/s when he passes ...
- Intro Physics Help - A runner in a relay race is required to run a distance of ...
- physics - Runner A is running at a constant rate of 2.3 m/s when he passes ...
- Physics - In a 5.00km race, one runner runs at a steady 11.6km/h and another ...
- physics - In an 8.00 race, one runner runs at a steady 11.8 and another runs at ...
- physics - A runner X ran the mile race in 4.25 sec. Another runner Y requires 4....
- Physics - Runner A is initially 6.0 km west of a flagpole and is running with a ...

More Related Questions