Question

Jason begins at the start of a path and rides his bike 11 1/2 miles on the path

Answer 1

Jason needs to ride 0.75 miles more to reach the end of the path

Solution:

Given that Jason begins at the start of a path and rides his bike $11\frac{1}{2}$ miles on the path

From given information,

$\text{Total length of path } = 12\frac{1}{4} \text{ miles } = \frac{4 \times 12 + 1}{4} = \frac{49}{4} \text{ miles }$

$\text{Distance covered already } = 11\frac{1}{2} \text{ miles } = \frac{11 \times 2 +1}{2} = \frac{23}{2} \text{ miles }$

To find: Distance in miles Jason must ride to reach the end of the path

Thus subtracting distance already covered from total distance, we get the distance Jason must ride to reach the end of the path

$\text{Distance needed } = \text{Total length of path } - \text{Distance already covered }\\\\\text{Distance needed } = \frac{49}{4} - \frac{23}{2}\\\\\text{Distance needed } =\frac{49}{4} - \frac{23 \times 2}{2 \times 2}\\\\\text{Distance needed } =\frac{49}{4} - \frac{46}{4} = \frac{49-46}{4} = \frac{3}{4} = 0.75$

Thus Jason needs to ride 0.75 miles more to reach the end of the path