Melissa and Rory live along a long street 21 km apart. They plan to meet at a park mid-way between their homes. They start out at the same moment, and ride toward each other at 7 km/hour. Melissa's dog Jessie knows this routine. He starts out with Melissa, and runs toward Rory at 18 km/hour. When he reaches Rory's bike, her turns around and runs toward Melissa. He reaches Melissa, turns around and runs toward Rory again...and so on, until Melissa and Rory meet. What distance did Jessie cover?
Please show steps.

Question

Melissa and Rory live along a long street 21 km apart. They plan to meet at a park mid-way between their homes. They start out at the same moment, and ride toward each other at 7 km/hour. Melissa's dog Jessie knows this routine. He starts out with Melissa, and runs toward Rory at 18 km/hour.  When he reaches Rory's bike, her turns around and runs toward Melissa. He reaches Melissa, turns around and runs toward Rory again...and so on, until Melissa and Rory meet. What distance did Jessie cover? 
Please show steps.

amistre64 · Answer

so one person is standing still and the other person is coming at them at 14 km and hour

amistre64 · Answer

but that might not be a fair conversion for the dog

amistre64 · Answer

21-7t = 18t

21 = 25t

21/25 = t hours so far;

anonymous · Answer

ok

amistre64 · Answer

21 - 7(21/25) - 7(21/25) = distance between them now

(231/25) - 7t = 18t

(231/25) = 25t

t = 231/625 hours to get back.

amistre64 · Answer

so far the dog has run:  18(21/25 + 21(11)/25^2)

and the distance left between the girls is:

21 - 14(21/25 + 21(11)/25^2); which when wolfram gets up and running i can calculate it better

amistre64 · Answer

ok, he runs 2 laps between them before they meet.

18(21/25) + 18(231/625) = distance run

amistre64 · Answer

21.7728 km

amistre64 · Answer

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