Question

Alphonse is training for a marathon. He runs 6 1/2 miles every 2/3 hour. How far does he run in 2 hours?

Answer 1

19 1/2 miles. Because you take 6 1/2 and divide that in half which is 3 1/4, so that is 1/3 of an hour. 3 1/4 times 3 is 9 3/4. Since that is only 1 hour you double that, which is 19 1/2.

Answer 2

`19.5\ miles` or
`19(1)/(2)\ miles`

Explanation:

we know that

Alphonse runs
`6(1)/(2)` miles every
`(2)/(3)` hour

so

by proportion

Find how far does he run in
`2` hours

Convert to an improper fraction first

`6(1)/(2)=(6*2+1)/2=13/2`

`((13/2))/((2/3))(miles)/(hours) =(x)/(2)(miles)/(hours) \\ \\x=(13/2)*2/(2/3)\\ \\x=39/2\\ \\x=19.5\ miles`

Convert to mixed number

`19.5\ miles=19+0.5=19+(1)/(2)=19(1)/(2)\ miles`