Last week, Shelly rode her bike a total of 45 miles over a three-day period. On the second day, she rode [tex]\frac{4}{5}[/tex] the distance she rode on the first day. On the third day, she rode [tex]\frac{3}{2}[/tex] the distance she rode on the second day. How many miles did Shelly ride on each day?

Question

31-08-2024
Mathematics

High School

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Last week, Shelly rode her bike a total of 45 miles over a three-day period. On the second day, she rode [tex]\frac{4}{5}[/tex] the distance she rode on the first day. On the third day, she rode [tex]\frac{3}{2}[/tex] the distance she rode on the second day. How many miles did Shelly ride on each day?

Answer :

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Final answer:

Shelly rode 15 miles on the first day, 12 miles on the second day, and 18 miles on the third day. This is calculated using her total distance and the ratios given for each day's distance.

Explanation:

Let's represent the distance that Shelly rode on the first, second and third days as x, 4x/5, and (3/2)*(4x/5), respectively. The total distance she rode for the three days is given as 45 miles, which can be translated into the equation x + 4x/5 + (3/2)*(4x/5) = 45. We can then solve this equation for x.

First, get rid of the fractions by multiplying the entire equation by 10, giving us 10x + 8x + 12x = 450. Combining like terms, we have 30x = 450. When we divide both sides by 30, we get x = 15.

So, Shelly rode 15 miles on the first day. On the second day, she rode 4x/5 = 12 miles, and on the third day, she rode (3/2)*(4x/5) = 18 miles. Therefore, the distances that Shelly rode on each day are 15 miles, 12 miles, and 18 miles respectively.

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