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LUCKY_DIMON [66]
3 years ago
12

Marcus can walk 1 mile to the library in about the same time he can bicycle 2.5 miles to the sporting good store. His speed on t

he bicycle is 6 mi/h faster than his walking speed What is Marcus's walking speed?
Mathematics
1 answer:
stira [4]3 years ago
5 0

Answer: Marcus's walking speed is 4 mph

Step-by-step explanation:

Let x represent Marcus's walking speed.

His speed on the bicycle is 6 mi/h faster than his walking speed. This means that his speed on the bicycle would be

x + 6

Time = distance/speed

Time spent by Marcus in walking 1 mile to the library is

1/x

Time spent by Marcus in bicycling 2.5 miles to the sporting good store is

2.5/(x + 6)

Since the time that he spends in walking to the library is about the same time that he spends in bicycling to the sporting good store, then

1/x = 2.5/(x + 6)

Cross multiplying, it becomes

1 × (x + 6) = 2.5 × x

x + 6 = 2.5x

2.5x - x = 6

1.5x = 6

x = 6/1.5 = 4

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Explanation
A) works; adding the two costs together is 250+145=395.  We multiply this by 0.85 because 100%-15%=85%=0.85.  We also have x% tax, which is represented by x/100, added to 100% of the value, or 1.00.  Altogether this gives us 
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B) works; we have 250+145 for the original price; we have 85% = 0.85 of the value; we also have 100% + x%, which is (100+x)/100.
C) does not work; (0.85+x/100)(395) does not take into consideration that you are finding the tax after taking the 85%.  This will simplify out to
0.85*395 + (x/100)(395) = 335.75 + 395x/100 = 335.75 + 3.95x, which is too much.
D) works; simplifying the expression from A, we have 395(0.85) + 395(0.0085x) = 335.75 + 3.3575x.
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