SOLUTION: Sara begins the race with a pace of 8 miles/hr. but gets tired after 15 min. and slows down to 4 miles/hr. Katy runs a steady pace of 5 miles/hr. the entire race. At what distan

Algebra ->  Customizable Word Problem Solvers  -> Travel -> SOLUTION: Sara begins the race with a pace of 8 miles/hr. but gets tired after 15 min. and slows down to 4 miles/hr. Katy runs a steady pace of 5 miles/hr. the entire race. At what distan      Log On

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Question 814532: Sara begins the race with a pace of 8 miles/hr. but gets tired after 15 min. and slows down to 4 miles/hr.
Katy runs a steady pace of 5 miles/hr. the entire race.
At what distance will katy pass sara?
Answer by josgarithmetic(39618) About Me  (Show Source):
You can put this solution on YOUR website!
Recognize two time periods: The first quarter of hour, and AFTER the first quarter of hour. The "AFTER" part is a variable time, call it h.

Sara: 8%2A%281%2F4%29%2B4%2Ah+=+d for some unknown distance d, based on the unknown time h.

Katy: The same steady speed the whole race, but for ALL of %281%2F4%29%2Bh hours of time.
5%281%2F4%2Bh%29+=+d

When Sara and Katy reach the same distance, their "d" is the same, and we can equation them and solve for h. Once h is found, use either equation to compute d. Start this with highlight%288%281%2F4%29%2B4h=5%281%2F4%2Bh%29%29
2%2B4h=5%2F4%2B5h
2=5%2F4%2Bh
h=2-5%2F4=2-1.25=highlight%280.75%29
This is three-quarters of an hour, or 45 minutes.

You still need to find the distance.