SOLUTION: Luis Nunez begins walking at a rate of 8 mph. Forty-five minutes after he​ leaves, his​ wife, Kristin, realizes that Luis has forgotten his wallet. Kristin gets on he

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Question 1091608: Luis Nunez begins walking at a rate of 8 mph.
Forty-five minutes after he​ leaves, his​ wife, Kristin, realizes that Luis has forgotten his wallet. Kristin gets on her bicycle and begins riding at a rate of
28 mph along the same path that Luis took.
a)how long will it take Kristin to catch luis?
b)how far from their house will Kristin catch luis?
Found 4 solutions by Boreal, addingup, MathTherapy, ikleyn:
Answer by Boreal(15235)   (Show Source): You can put this solution on YOUR website!
distance=speed*time
Luis will be caught t hours after he started walking, at a distance of 8t miles.
Kristin will catch Luis at a distance of 8x miles. Her speed is 28 mph, so 28*(t-0.75)=8t, since her time is 3/4 of an hour less.
28t-21=8t
20t=21
t=21/20 hours , or 63 minutes; Kristin started 45 minutes later, so it took her 18 minutes to catch him.
in that time, Luis will have walked 8 mph*1.05 hours=8.40 miles; Kristin will have ridden 28 mph*18 minutes or 0.3 hours, and that is 8.4 miles.
Answer by addingup(3677)   (Show Source): You can put this solution on YOUR website!
45/60 = 75% 45 minutes is 75% of an hour (an hour has 60 minutes)
80*0.75 = 6 Luis walked 6 miles in 45 minutes
6/28 = 0.2143 and 60*0.2143 = 12.858 minutes.
Kristin will catch up with Luis in just under 13 minutes.
Answer by MathTherapy(10555)   (Show Source): You can put this solution on YOUR website!
Luis Nunez begins walking at a rate of 8 mph.
Forty-five minutes after he​ leaves, his​ wife, Kristin, realizes that Luis has forgotten his wallet. Kristin gets on her bicycle and begins riding at a rate of
28 mph along the same path that Luis took.
a)how long will it take Kristin to catch luis?
b)how far from their house will Kristin catch luis?
Let time Kristin takes to get to catch-up point, be T

Then time Luis takes to get to catch-up point = 

We then get the following DISTANCE equation: 

28T = 8T + 6

28T - 8T = 6

20T = 6

T, or time Kristin takes = 

Distance traveled from house to catch-up point: 

IGNORE that person who claims the time to be about 13 minutes. Most times he/she does NOT HAVE a clue.

Everyday, I wonder what they're doing on here, because they're not helping, but compounding people's math anxiety by giving them WRONG answers, most times. 

He/she is yet to realize that most times, his/her answers just DO NOT ADD UP. I wonder if he/she will EVER realize that. 

Answer by ikleyn(52832)   (Show Source): You can put this solution on YOUR website!
 .

On catching-up problems, see the lesson



    - Travel and Distance problems for two bodies moving in the same direction (catching up) 



in this site.







------------

This is how to solve this problem MENTALLY (without using equation).






In 45 minutes Luis will be in  = 6 miles from the home.

So, the distance between him and Kristina was 6 miles when Kristina started her move.

Their relative speed is 28 - 8 = 20 mph.

It means that the distance between them increasing at the rate of 20 mph.

Hence, the time to catch up is  =  hours = 18 minutes.





Solved.







 

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