Question

You are one mile from the railroad station, and your train is due to leave in eight minutes. You have been walking at a quick rate of 4 mph, and you can run at 9 mph if you have to. For how many more minutes can you continue walking, until it becomes necessary for you to run the rest of the way to the station?

Answer 1

@phi

Answer 2

Shouldn't it depends on how far are you currently from the station?

Answer 3

perhaps

Answer 4

Oh, it says it ... omg, I'm blind.
I mile away:)

Answer 5

So, all the time you have is 8 minutes. Every minute (with 4mph) you complete \(\color{black}{\displaystyle \frac{1}{15}{\rm miles}}\). So, obviously if you walk like this all 8 minutes you won't get to the train. (Which is especially bad after 8:30pm)

Answer 6

if you start running 9mph, you are going \(\color{black}{\displaystyle \frac{3}{20}{\rm miles}}\) every minute.

Answer 7

\(\color{black}{\displaystyle \frac{1}{15}x+\frac{3}{20}y=1}\)

\(\color{black}{\displaystyle x+y=8}\) and \(\color{black}{\displaystyle x,y>0}\)

where x is the number of minutes you go 4mph, and y is the number of minutes you run 9mph.

Answer 8

*x is the number of hours
we will have to change it to minutes

Answer 9

it sounds like you want an equation like
4 x + 9(8/60 -x) = 1
where x is the number of minutes you can walk

Answer 10

4x + 72/60 - 9x = 1
-5x + 6/5 = 1
-5x = -1/5
x = 1/25

Answer 11

getting the units correct is the hardest part.

x= 1/25 is in hours (because speed is in miles per hour)
multiply by 60 to get minutes

Answer 12

x would be hrs

Answer 13

yeah got that thanks :)