Question 1011621: 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 ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! 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?
:
change 15 min to .25 hrs ( we're dealing in km/hr)
let t = time spent walking in hrs
then
(.25-t) = time spent running in hrs
:
Write a distance equation; dist = speed * time
walk dist + run dist = 2 km
5t + 15(.25-t) = 2
5t + 3.75 - 15t
5t - 15t = 2 - 3.75
-10t = -1.75
t = -1.75/-10
t = +.175 hrs walking
How far can he walk in this time?
5 * .175 = .875 km walking before he has to run 1.125 km
:
:
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?
:
That means he has 3 more minutes to catch the bus at B, or 18 min
Change 18 min to hrs, 18/60 = .3 hrs
:
let t = time spent walking in hrs
then
(.3-t) = time spent running in hrs
:
Write a distance equation; dist = speed * time
walk dist + run dist = 2 km
5t + 15(.3-t) = 2
5t + 4.5 - 15t
5t - 15t = 2 - 4.5
-10t = -2.5
t = -2.5/-10
t = +.25 hrs walking
How far can he walk in this time?
5 * .25 = 1.25 km walking before he has to run .75 km
Find how much less running 1.125 - .75 = .375 km less running
:
:
See if that checks out. find the distance walking and distance running
walking: .25*5 = 1.25 km
running: (.3-.25)*15 = .75 km
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Total distance: 2 km
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