First, we note that 440 yards is equivalent to 0.25 miles.
To answer the problem, we first try to visualize what's happening.
There are two runners, A and B. The speed of A is 8mph, that of B is 10 mph. A and B are standing on opposite ends of a track that is 0.25 miles long. They are running towards each other. Now, since they are running towards each other, they will definitely meet. The point of meeting is important -- it will be at the same point (of course) and they would have ran after the same amount of time (of course, assuming they started at the same time).
A --------x-------------------B
In the illustration above, x would be the meeting point. Obviously, B would have covered more distance since he has a greater speed. Assuming A covered a distance of x miles, B would have covered a distance of 0.25 - x miles (since the total distance is 0.25 miles. Also, note that we could have assigned x to B and 0.25-x to A but that would not affect the answer). Then, we let the total time lapsed equal to y. The time is equal for both runners.
To summarize our variables:
Speed of A: 8 mph
Speed of B: 10 mph
Distance Travelled by A: x miles
Distance Travelled by B: 0.25 - x miles
Time A Ran: y
Time B Ran: y
Next, we note that speed is simply distance over time. From the given, we can obtain two equations:
`x/y = 8`
`(0.25 - x )/ y = 10`
The first equation is simply `x = 8y` . The second equation reduces to `0.25 - x = 10y` , which, using equation one, can be easily solved as: `0.25 - 8y = 10y rightarrow 0.25 = 18y` . This means that `y = 0.25/18 =0.013888889 hrs` , which is just 50 seconds.` `
Hence, the runners will meet after 50 seconds.
---
To check, simply solve for the distance travelled by both after 50secs or 0.01389 hours.
Distance (A) = 8 mph * 0.01389 h = 0.11112 miles
Distance (B) = 10 mph * 0.01389 h = 0.1389 miles
Total (A+B) = 0.11112 + 0.1389 = 0.25 miles
The answer must be correct. The total distance is 0.25 miles, and hence the two must have met. Also, B travelled more distance since s/he is faster. If they had the same speed, they would simply meet at the center.
We’ll help your grades soar
Start your 48-hour free trial and unlock all the summaries, Q&A, and analyses you need to get better grades now.
- 30,000+ book summaries
- 20% study tools discount
- Ad-free content
- PDF downloads
- 300,000+ answers
- 5-star customer support
Already a member? Log in here.
Are you a teacher? Sign up now