Two stations, A and B, are located six miles apart on a railroad. The rates of cartage of coal are 50 cents per ton per mile from A and 75 cents per ton per mile from B. At a certain consumer's home, located on the railroad between A and B, the cost for cartage is the same whether the coal is delivered from A or from B. Find the distance from this home to A.

a. 3 miles
b. 3 1/2 miles
c. 3 3/5 miles
d. 4 miles
e. 4 1/2 miles

please answer and explain

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  1. cost is rate * distance. If the distance from home to A is x, then from home to B is 6-x. So, since the costs are the same,

    50x = 75(6-x)
    50x = 450-75x
    125x = 450
    x = 3.6

    So, (C)

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