Morgan left home at 7:00 one morning, determined to make the ten-mile trip to schoool on bicycle for a change. Soon thereafter, a parent noticed forgotten math homework on the kitchen table, got in the car, and tried to catch up with the forgetful child. Morgan had a fifteen minute head start and was pedaling at 12 mph, while the parent pursued at 30 mph.
Was Morgan reunited with the homework before reaching school that day ? If so, where? If not at what time during the first period( math, which starts at 8:00) was the homework delivered?

I tried to start with where Morgan would be at 7:15.

At 7:15 Morgan would have traveled 3 miles of the ten mile trip.

And now I am stuck.

Vicky

Use d = rt.

If t = number of hours since 7:00, then the equation for Morgan is
.

The equation for the parent, taking into account that he/she leaves 0.25 hr (15 min) after Morgan, is
.

We want to know after how many miles to the two meet, so set , or

and solve for t:



So Morgan will meet the parent at 7:25, 5 miles () from their house.


01

If Morgan is travelling at 12mph, that means she travels 12miles in 60 mins. This is the same as of a mile every minute.

If she has 10 miles to travel, it will take 50 minutes (since she travels 1 mile every 5 minutes).


If Morgan's mother is travelling at 30mph, that means she travels 30 miles in 60 mins. This is the same as travelling a mile every minute.

If she has 10 miles to travel, it will take 20 minutes (since she travels 1 mile every 2 minutes).


Obviously, with only 15 minutes head start, Morgan's mother will still beat her to the school.


I'll let you try to figure out when and where they meet.

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Two things are infinite - The Universe and Human Stupidity. Though I'm not too sure about the universe...

An alternative approach to those already given:

The velocity of parent relative to child is 18 mph. Using d = vt, parent catches up to child in time t such that 3 = 18t => t = 1/6 hour = 10 minutes. Knowing the time makes it simple to calculate where they meet.

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What about Zeno (?) and the tortoise?

What about them? That 'paradox' was resolved a long time ago and can be read about at any one of the thousands of websites found by Google.

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Twas a joke, Mr. Funniest member! :P

You really are quite something.

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