SOLUTION: Grade 8 math word problem Bus station is 10km away. To catch bus before it leaves, you must travel a rate of 60km/hr by car to get there. There is bad weather so you're only abl

Question 847160: Grade 8 math word problem
Bus station is 10km away. To catch bus before it leaves, you must travel a rate of 60km/hr by car to get there. There is bad weather so you're only able to drive 30km/hr for the first 5km. What speed must you travel the rest of way to catch the bus?
What I'm thinking so far...
If you should drive 60km/hr, then 1km should take 1 min (60 divided by 60). Therefore it should normally take 10mins to get there.
30km/hr divided by 60 would mean you traveled 0.5km/min. So 0.5 x 10= 5km for 10mins. Now what?
Found 2 solutions by ankor@dixie-net.com, josgarithmetic:
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
Bus station is 10km away.
To catch bus before it leaves, you must travel a rate of 60km/hr by car to get there.
There is bad weather so you're only able to drive 30km/hr for the first 5km. What speed must you travel the rest of way to catch the bus?
:'
It will be impossible to catch the bus, AT 60 km/hr the time required would be
= 1/6 hrs or 10 min
AT 30 km/hr the time for you to go 5km
= 1/6 hr or about 10 min
Another words, you've used up the 10 min already
Answer by josgarithmetic(39630) (Show Source): You can put this solution on YOUR website!
NORMALLY, the situation would conform to RT=D, , hours which is ten minutes. The rest of the description in your problem seems consistant with staying with this same total ten minute time quantity. "you're only able to drive 30km/hr for the first 5km. What speed must you travel the rest of way to catch the bus?"

DATA TABLE--------------------------------------

_________________speed__________time_________distance
Bad Weather______30_____________(___)___________5
Improved Wthr____r______________(___)__________(___)
TOTAL__________________________________________10

We want to find r, the speed to be used in the improved weather, to keep with the total time of hour for the total trip distance of 10 kilometers. We fill in the missing time slots using (the concept, not the actual variables I'm using).

_________________speed__________time_________distance
Bad Weather______30_____________()___________5
Improved Wthr____r______________()__________(5)
TOTAL_______________________________________10

The total time sum gives the equation in the single variable, r, which we want to solve.

MOST of the solution process (usually) is to analyze the information and formulate that equation. The rest of the process is just arithmetic. The trouble is that in trying to simplify that equation on your way to solve for r, you will find:

------This will not work.
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In the practical sense, the driver going at 30 km/hour for the first 5 km, has run out of time. The driver WILL be late on the trip! What this driver must do is to LEAVE TEN MINUTES (ONE SIXTH HOUR) EARLIER!
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Notice also, with the bad weather, the speed was cut in half? This means twice as much time is needed than in the good weather.
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