Question

Any traveled \(\frac{4}{7^{th}}\) as many miles on foot as by water and \(\frac{2}{5^{th}}\) as many miles on horse back as by water. If she covered a total of 3036 miles, how many miles did she travel in each manner: water, foot and horseback?

• A. 1540, 880, 616
• B. 616, 880, 1540
• C. 1540, 616, 880
• D. 880, 1540, 616

Answer 1

The Correct Option is A

Let the distance traveled by water be x miles. The distance on foot is \(\frac{4}{7}\) times the distance by water, which can be expressed as \(\frac{4}{7}x\). The distance on horseback is \(\frac{2}{5}\) times the distance by water, which is \(\frac{2}{5}x\).

The total distance covered is 3036 miles, thus we have the equation:

\(x + \frac{4}{7}x + \frac{2}{5}x = 3036\)

To solve this equation, find a common denominator for the fractions involved, which is 35. Rewrite the fractions:

\(\frac{4}{7}x = \frac{20}{35}x\)

\(\frac{2}{5}x = \frac{14}{35}x\)

Now, rewrite the equation with these fractions:

\(x + \frac{20}{35}x + \frac{14}{35}x = 3036\)

Add the fractions:

\(\frac{35}{35}x + \frac{20}{35}x + \frac{14}{35}x = \frac{69}{35}x\)

The equation becomes:

\(\frac{69}{35}x = 3036\)

Solve for x by multiplying both sides by \(\frac{35}{69}\):

\(x = 3036 \times \frac{35}{69}\)

Calculating this gives:

\(x = 1540\)

Therefore, the miles traveled by water are 1540. Calculate the miles traveled on foot and horseback:

Foot: \(\frac{4}{7} \times 1540 = 880\)

Horseback: \(\frac{2}{5} \times 1540 = 616\)

Thus, Any traveled 1540 miles by water, 880 miles on foot, and 616 miles on horseback. The correct option is:

1540, 880, 616