Question

help me please!!! :)

it took a faster runner 10 seconds longer to run a distance of 1500 ft than it took a slower runner to run a distance of 10000 ft if the rate of the faster runner was 5 ft/sec more than the rate of the slower runner what was the rate of each?

Answer 1

i got 2 answers for x. x=20 and x=25..

Answer 2

This question doesn't make sense. Do you mean the faster runner ran 1500 ft 10 seconds longer than the slow runner ran 1000 ft? (vs. 10,000 ft?)

Answer 3

ooops! sorry. yeah, that should be 1000 ft..pls help me

Answer 4

Let A be the speed of the fast runner in ft/sec. And B the speed of the slow runner.

Then the time the fast runner ran 1500 ft is 1500/A, and the slow runner 1000ft is 1000/B.
Because speed = distance/time => time = distance/speed

Agreed so far?

Answer 5

can i equate the two equations like this:

1000/B = (1500/A) - 10

????

Answer 6

Yes exactly. That's the first equation.

Now what's the second equation in terms of A and B

Answer 7

uhm..

1000/B = (1500/B+5) - 10

???

Answer 8

because A=B+5

Answer 9

Yes. Now solve.

Answer 10

And now I see your problem. After solving I also get B = 20 or 25, and hence A = 25 or 30 respectively.

Let's check. Suppose A = 30, B = 25. Then fast runner time = 1500/30 = 50 sec; slow runner time = 1000/25 = 40 seconds, so that works.

Now A = 25, B = 20. Fast runner time = 1500/25 = 60 sec. Slow runner time = 1000/20 = 50 sec.

So yes, both solutions are correct.

Answer 11

Not obvious there would be two solutions.

Answer 12

thank you sir!