SOLUTION: If Bill rides his bike 3 mi to Fred's house and then walks with Fred the remaining 1 mi to school, it will take him 30 min. But if he rides the entire distance, it will take him on

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Question 174710: If Bill rides his bike 3 mi to Fred's house and then walks with Fred the remaining 1 mi to school, it will take him 30 min. But if he rides the entire distance, it will take him only 20 min. Find his biking speed and walking speed.
for this equation, i tried to set the problems up like this:
3 b + 1 w= 30 min
b = 20 min
3(20) + 1 w = 30
60 + 1 w = 30
-60 -60
1 w = -30
I would like to see if this is a correct way to work. If not, then please assist me. I would really appreciate it!!
Found 2 solutions by stanbon, Mathtut:
Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website!
If Bill rides his bike 3 mi to Fred's house and then walks with Fred the remaining 1 mi to school, it will take him 30 min. But if he rides the entire distance, it will take him only 20 min. Find his biking speed and walking speed.
for this equation, i tried to set the problems up like this:
3 b + 1 w= 30 min
b = 20 min
3(20) + 1 w = 30
60 + 1 w = 30
-60 -60
1 w = -30
==============================
Bill DATA:
Bike:
distance = 3 mi ; rate = b mph ; time = d/r = 3/b hrs
Walk:
distance = 1 mi : rate = w mph ; time = d/r = 1/w hrs
---
Bill equation:
time + time = (1/2) hr
(3/b) + (1/w) = 1/2
============================
Bill DATA:
distance = 4 mi; rate = b mph ; time = 4/b hrs
Bill/bike equation:
4/b = (1/3) hr
b/4 = 3
b = 12 mph (speed at which Bill bikes)
----------------
Substitute into (3/b) + (1/w) = 1/2 to solve for "w"
3/12 + 1/w = 1/2
1/w = 1/4
w = 4 mph (speed at which Bill walks)
=======================================
Cheers,
Stan H.

Answer by Mathtut(3670) (Show Source):
You can put this solution on YOUR website!
lets call Rate walkingand rate biking
:
d=rt
:
............20 min =1/3 hr
:
mph
:
so for the bike to travel 3 miles lets find the time
:
3=12t--->t=3/12=1/4 hr
:
so if the total time for biking and walking is 1/2 hr
:
then the time for walking 1 mile is 1/4 hr(1/2-1/4)
:

:
mph