SOLUTION: John can walk at 5 km/h and run at 15 km/h. A and B are two stops on a road. Both are 2 km from John’s home. a) The bus leaves from A in 15 minutes. How far can John walk from hom

Algebra ->  Finance -> SOLUTION: John can walk at 5 km/h and run at 15 km/h. A and B are two stops on a road. Both are 2 km from John’s home. a) The bus leaves from A in 15 minutes. How far can John walk from hom      Log On


   

Question 1011612: John can walk at 5 km/h and run at 15 km/h. A and B are two stops on a road. Both are 2 km from John’s home.
a) The bus leaves from A in 15 minutes. How far can John walk from home before he has to run to catch the bus?
b) It takes the bus 3 minutes to travel from A to B. If John catches the bus at B, how much less running does John have to do?
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
(a)
John's travel on foot is in two parts: Walk and Run. These two parts will total 2 kilometers. Sum of the time will be 1%2F4 hour.

x, time walking
y, time running
system%285x%2B15y=2%2Cx%2By=1%2F4%29
Solve for x and y.
Now evaluate 5x, the answer to this question.

--
The solved system will be x=7%2F40 hour and y=3%2F40 hour;
and the distance gone by walking before need to run is 5%287%2F40%29=%287%2F8%29%2Akilometer.


(b)
This is 18 minutes alloted time, or 18%2F60=3%2F10 of hour.
The system is now system%285x%2B15y=2%2Cx%2By=3%2F10%29.
Solve this to find x=1%2F4 which is 15 minutes, and y=1%2F20, which is 3 minutes of running.