SOLUTION: Jim lives 70 miles from work. He rides his bike at 6 mph to the metro station. He then takes the metro to work, which travels at 59 mph. If he spends 45 minutes more on the bike

Question 677140: Jim lives 70 miles from work. He rides his bike at 6 mph to the metro station. He then takes the metro to work, which travels at 59 mph. If he spends 45 minutes more on the bike than on the metro, what is the distance from his work to the metro station?
This is the kind of word problem I have had the most trouble conceptualizing in my mind. Firstly, its out to convert minutes to time, so I've attempted this, below. The formula should be D=RT,because they I'm being asked to solve the distance. In my set up, I put 49 minutes over 60 minutes to represent minutes over hours.
6(x + 49/60) + 59x = 70
I then distributed the left side and converted the fraction into a decimal by dividing 49 into 60. My calculator said .816. I assumed I should round my answer to the nearest tenth (is that something I should be doing?), because I get two answers. With .816, I get 6 x .816 = 4.896, with .81, I get 6 x .81 = 4.86 and with the rounded to the nearest tenth, I 6 x .85 = 5.1 THREE completely different answers! So, I'll stick with .81 to see what happens.
6x + 4.86 +59x = 70
Next, I combine like terms.
65x = 65.14
Lastly I divide the variable on both sides.
On my calculator, it says the total is 1.0
x = 1.0
Then, I plugged 1.0 into the metro 59x to make 59(1.0) = and I got 59.
This doesn't seem right to me. Can you help me find out what it is I need to know?

Answer by josmiceli(19441) (Show Source): You can put this solution on YOUR website!
Just call 45 min 3/4 hr
You need 2 equations, one for home to Metro
and one for Metro to work
Let = the distance from Metro to work
= the distance from home to Metro
Let = time spent on Metro
= time spent on bike ( home to metro )
-------------------
Equation for home to Metro:
(1)
Equation for Metro to work:
(2)
---------------
(1)
Substitute (2) into (1)
(1)
(1)
(1)
(1) hrs
and
(2)
(2)
(2)
(2)
From work to Metro is 59.454 mi
check answer:
(2)
(2)
(2)
(2)
and
(1)
(1)
(1)
(1)
(1)
OK
Hope I got it

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