Question 795681: "2. Two cyclists start biking from a trail's start 3 hours apart. The second cyclist travels at 10 miles per hour and starts 3 hours after the first cyclist who is traveling at 6 miles per hour. How much time will pass before the second cyclist catches up with the first from the time the second cyclist started biking?"
This is the answer explanation I looked up: Let D = Distance where they (Mr. A & Mr. B) will meet. H = Hours A has traveled by the time they meet.
For A: D = 6 mi/hr (H) = 6H
For B: D = 10 mil/hr (H-3) = 10H - 30; note: Because B starts 3 hours after A, thus he will travels 3 hours less than A's which represented by H.
now, Since they have the same D, we equalize 2 equations as below,
10H - 30 = 6H
==> 10H - 6H -30 = 0
==> 4H - 30 = 0
==> 4H = 30
==> H = 7.5 hours which is to say they will meet in 7.5 hrs after A travels, and the distance D whre they will meet would be 6 mi/hr (7.5 hrs) = 45 miles.
So what I don't understand is the "6 mi/hr (7.5 hrs)= 45 miles". Did they multiple the 7.5 and 6? Cause that's not 45. Or did they divide it? I'm just really confused on this. It's causing me a lot of strife. Please reply soon!
Thank You!!
Dominique, HS Junior
Answer by MathTherapy(10556)   (Show Source):
You can put this solution on YOUR website!
"2. Two cyclists start biking from a trail's start 3 hours apart. The second cyclist travels at 10 miles per hour and starts 3 hours after the first cyclist who is traveling at 6 miles per hour. How much time will pass before the second cyclist catches up with the first from the time the second cyclist started biking?"
This is the answer explanation I looked up: Let D = Distance where they (Mr. A & Mr. B) will meet. H = Hours A has traveled by the time they meet.
For A: D = 6 mi/hr (H) = 6H
For B: D = 10 mil/hr (H-3) = 10H - 30; note: Because B starts 3 hours after A, thus he will travels 3 hours less than A's which represented by H.
now, Since they have the same D, we equalize 2 equations as below,
10H - 30 = 6H
==> 10H - 6H -30 = 0
==> 4H - 30 = 0
==> 4H = 30
==> H = 7.5 hours which is to say they will meet in 7.5 hrs after A travels, and the distance D whre they will meet would be 6 mi/hr (7.5 hrs) = 45 miles.
So what I don't understand is the "6 mi/hr (7.5 hrs)= 45 miles". Did they multiple the 7.5 and 6? Cause that's not 45. Or did they divide it? I'm just really confused on this. It's causing me a lot of strife. Please reply soon!
Thank You!!
Dominique, HS Junior
6(7.5), or 6 * 7.5 is INDEED 45, or 45.0 if you want to get technical, which by the way, is 45. Multiply it manually or with a calculator.
You can do the check!!
Send comments, “thank-yous,” and inquiries to “D” at MathMadEzy@aol.com. Further help is available, online or in-person, for a fee, obviously.
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