SOLUTION: Tom's home is 1,800 m from his school. One morning he walked part of the way to school and then ran the rest. If it took him 20 minutes or less to get to school, and he walks at 70

Question 179569: Tom's home is 1,800 m from his school. One morning he walked part of the way to school and then ran the rest. If it took him 20 minutes or less to get to school, and he walks at 70m/min and runs 210m/min, how far did he run?
Answer by josmiceli(19441) (Show Source): You can put this solution on YOUR website!
I will write 2 equations:
1 for running
1 for walking
(1)
(2)
given:
m/min
m/min
m
min
--------------------------
I can rewrite (1) and (2):
(1) m
(2) m
Now, from
I get

I'll substitute this in (2)
(2) m
{2) m
I'll subtract (1) from (2):
{2)
(1)

Divide both sides by
(3)
from
min
If min
Multiply each side by
(4) min
Subtract (4) from (3)
(3)
(4)

min
and,since
min

min
The problem wants to know how far he ran
(2) m
m
m
He ran 600 m
check answer:
I can rewrite (1) and (2):
(1) m
m
m
And, since
m

OK
I also looked at
min
If he spent a little more time running than
walking, say

and

m
If he spent a little more time walking than running

m
So, he has to spend at least as much time running
as he did
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