SOLUTION: In Linear Equation Homework: "Matt loves biking. He bikes uphill at 4 mph, downhill at 6 mph, and manages to cover 18 miles in 4 hours. How many miles did he bike downhill?" I n

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Question 911750: In Linear Equation Homework:
"Matt loves biking. He bikes uphill at 4 mph, downhill at 6 mph, and manages to cover 18 miles in 4 hours. How many miles did he bike downhill?"
I normally have problems with speed, distance and time. I thought maybe 18/4= something. I don't know what to do with the 4 mph and 6 mph. I know I ought to add them or something similar, but I can't decide about the mph part. Does the unit cause the question to differ? I simply can't put one end with the other.
Thanks.
Found 3 solutions by josgarithmetic, MathTherapy, richwmiller:
Answer by josgarithmetic(39626)   (Show Source): You can put this solution on YOUR website!
Being a travel problem with simple rates and distance,
RT=D uniform rates rule for travel, RATE, TIME, DISTANCE.

4 mph uphill and 6 mph downhill.
18 miles in 4 hours.

Some thinking...

Nothing comes into mind easily. Try making a table of data.

______________rate___________time__________distance
UPHILL________4_______________x
DOWNHILL______6_______________y

Notice the assigning of variables for times.


Use RT=D idea to put in expressions for distances.

______________rate___________time__________distance
UPHILL________4_______________x____________4x
DOWNHILL______6_______________y____________6y


You were given the total time and total distance.

______________rate___________time__________distance
UPHILL________4_______________x____________4x
DOWNHILL______6_______________y____________6y
Totals________________________4____________18

You may be able to now see what next to do. Tell me if you still have trouble continuing from this data table.
Answer by MathTherapy(10556)   (Show Source): You can put this solution on YOUR website!

In Linear Equation Homework:
"Matt loves biking. He bikes uphill at 4 mph, downhill at 6 mph, and manages to cover 18 miles in 4 hours. How many miles did he bike downhill?"
I normally have problems with speed, distance and time. I thought maybe 18/4= something. I don't know what to do with the 4 mph and 6 mph. I know I ought to add them or something similar, but I can't decide about the mph part. Does the unit cause the question to differ? I simply can't put one end with the other.
Thanks. 


Let distance he biked downhill be D

Then distance biked uphill = 18 – D

We then get: D/6 + (18 - D)/4 = 4

2D + 3(18 – D) = 48 ------- Multiplying by LCD, 12 

2D + 54 – 3D = 48 

2D – 3D = 48 – 54 

- D = - 6

D, or distance biked, downhill = , or  miles

You can do the check!! 

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Answer by richwmiller(17219)   (Show Source): You can put this solution on YOUR website!
 x+y=4

x=4-y

r*t+r*t=d



4x+6y=18

4*(4-y)+6y=18

16-4y+6y=18

16+2y=18

2y=2

y=1

x=4-1=3



6*1=6 miles downhill

4*3=12 miles uphill

 

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