Okay. bicyclists. start 3 hours apart. you want to know when they meet, so you want to know when the distance is the same.

distance = rate x time

So, bicyclist 1, let’s call him “A” … “A” = 6 mph x time
An’ bicyclist 2, let’s call him “B” … “B” = 10 mph x (time – 3)
The minus 3 is cuz he’s travelin’ 3 hours less than the other one. Now, because “A” = “B” (they’ve gone the same distance when they meet), you’ve got an equation your can solve:

6 x time = 10 x (time – 3) … that’s the same as: 6t = 10(t – 3)

Now, it’s jus’ algebra, right? you multiply the 10 by both the “t” and the 3…

6t = 10t – 30

Now, subtract 10t from both sides to get the “t”s all together… remember, cuz it’s minus 30, your 30′s gonna be negative:

6t – 10t = -30
-4t = -30

Now, divide by -4 to get t all by itself… a negative divided by a negative is a positive, which is good, otherwise they’d be time travelin’ into the past!

t = -30/-4 = 7.5 hours

Now, in what I wrote, “t” is the time of the first cyclist. t – 3, or 4.5 hours is the time from when the second cyclist starts to when he catches up. I ain’t too sure, the way the question’s worded, which time it wants. Read the original again an’ see if you can figure it out… is it from when the first guy starts or from when the second guy starts?

Now, the time seems pretty reasonable, but…. let’s check. First cyclist goes for 7.5 hours at 6 mph, that’s 45 miles. Second cyclist goes for 4.5 hours at 10 mph, that’s 45 miles, too. There’s your answer. It’s 7.5 hours from when the first guy started, and 4.5 hours from when the second guy started.

Dat makes sense for me . I never thought it’s that easy . As soon as you get the time the dog ran between them , then it’s easy for you to calculate the distance . Don’t you think we can solve it this way :

She started to walk at 4 mph , while there are 2 miles distance between them . Well , dat means she only needs one hour to overtook the man . ( 2 miles distance between them + the 2 miles the man walked ) . Total time for dog is : 1 hour and now we’re done with it . d = rt . d = 5mph x 1hour = 5 miles distance the dog ran .

Thank you very much for your continued support dear Curtis . I will contact you again for another one if you don’t mind ..

Zaher