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

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) (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: for some unknown distance d, based on the unknown time h.

Katy: The same steady speed the whole race, but for ALL of hours of time.

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

This is three-quarters of an hour, or 45 minutes.

You still need to find the distance.
RELATED QUESTIONS
If Katy runs at a pace of 4 mph, how many miles can she run in 8 hours? (answered by jim_thompson5910)

Need equation:Jane leaves school and walks home at a rate of 4 mi/hr. 15 minutes later,... (answered by josmiceli)

Dianna runs a race of 2 miles in 8 minutes at a steady speed. Each mile she runs beyond 2 (answered by ankor@dixie-net.com)

you run a 10 mile race by running at a pace of 8 minutes per mile for 1 hour, and after... (answered by josgarithmetic)

There are 2 runners. One runs 15.15 miles in 2 hours and 37 minutes with a pace of 10:23... (answered by Boreal)

Andrew participated in a bicycle race. The total distance covered was 56 miles. If he... (answered by rapture)

Lou can walk the 2 1/2 miles to school at the rate of 6 mph, or ride his bike at 12 mph.... (answered by josgarithmetic,MathTherapy)

A woman begins jogging at 3:00 P.M., running due north at a 6- minute- mile pace. Later,... (answered by stanbon,ankor@dixie-net.com)

in a race from point X to point Y,bilal averages 30 miles/hr to point Y and 10 miles/hr... (answered by edjones)