SOLUTION: I can not figure out the formula to use for the following word problem. I have tried the d=rt but I do not have the time or the rate of movement. I also tried dividing the total d

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Question 986249: I can not figure out the formula to use for the following word problem. I have tried the d=rt but I do not have the time or the rate of movement.
I also tried dividing the total distance by the cost per gal.
Two gas distributors in Interstate 80 are 228 miles apart. A sells gasoline at 3.40 per gal. B sells it for 3.20 per gal both charge .2 cents per gal per mile for delivery. Where on Interstate 80 is the cost the same to the customer?
Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39618) About Me  (Show Source):
You can put this solution on YOUR website!
Imagine a point X between A and B, and x is the length AX. If AX is the length x, then the other length XB is 228-x.

The description and question give no information about how many gallons any of the two distributors will sell, so just assume a quantity G gallons which either distributor A or B will sell to the station at X.

COST from Distributor A
3.4G%2B%280.002%29%2AG%2Ax-----think about the last term a little and it should make sense;

COST from Distributor B
3.2G%2B%280.002%29%2AG%2A%28228-x%29

For which value of x will costs for A and B be the same or equal?
3.4G%2B%280.002%29Gx=3.2G%2B%280.002%29G%28228-x%29
TRY to isolate and solve for x.
3.4G%2B0.002Gx=3.2G%2B0.456G-0.002Gx
3.4G%2B0.002Gx%2B0.002Gx=3.2G%2B0.456G
0.004Gx=3.2G%2B0.456G-3.4G
Divide left and right members by the constant, G;
0.004x=3.2-3.4%2B0.456
0.004x=-0.2%2B0.456
highlight%28x=64%29

Station X should be placed 64 miles away from distributor A, between A and B. This will make purchase cost from A equal to that from B.

The problem uses two kinds of rates, both related to distance. TIME is not part of this problem. You deal with volume distance and money here.

Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!

I can not figure out the formula to use for the following word problem. I have tried the d=rt but I do not have the time or the rate of movement.
I also tried dividing the total distance by the cost per gal.
Two gas distributors in Interstate 80 are 228 miles apart. A sells gasoline at 3.40 per gal. B sells it for 3.20 per gal both charge .2 cents per gal per mile for delivery. Where on Interstate 80 is the cost the same to the customer?
Let distance from customer be D

Then: 3.4 + D(.002) = 3.2 + D(.002)

3.4 + .002M = 3.2 + .002(228 - M)

3.4 + .002M = 3.2 + .456 - .002M

.002M + .002M = 3.2 - 3.4 + .456

.004M = .256

M, or distance = .256%2F.004, or 64 miles



This means that distributor A should be positioned closer to the customer, or highlight_green%2864%29 miles from the customer, since this distributor's gas price is higher

Thus, distributor B should be positioned farther or highlight_green%28164%29 (228 - 64) miles from the customer, since this distributor's gas price is the lesser of the two.