Question

Solve. Enter your answer as a mixed number. The driving distance from Alex's house to the museum is 6 9 10 miles. What is the round-trip distance? The round-trip distance is miles.

Answer 1

The round trip distance is =
`13(8)/(10)`

Explanation:

Round trip here refers to the distance that Alex covered while driving to the museum from his house in addition to the distance that he covered as he returned home from the museum. That is the sum of the distance he covered while going and returning to his base.

Now, if Alex covered a total distance of 6 9/10 miles while journeying to the museum and then covered the same distance while returning (6 9/10), we can calculate his round trip distance by adding the distances covered while going and returning.

That is, the round trip distance for Alex's to and fro journeys is:

`6(9)/(10) + 6(9)/(10)`

We pick out the whole numbers and then add them up first

6 + 6 = 12

Then the fractions

9/10 + 9/10 = 18/10

We now have:

`12(8)/(10)`

Which is
`12(10 + 8)/(10)`

Since 10/10 = 1

Then:

`(12 + 1) (8)/(10)`

=
`13(8)/(10)`

We can also convert the two fractions into improper fractions and then solve. That is:

`6(9)/(10) = ((10*6)+9)/(10) = (69)/(10)`

= 69/10

adding up the two distances covered while journeying to the museum and returning, we have:

69/10 + 69/10

= 138/10

That is 13 remainder 8

=
`13(8)/(10)`

This means that Alex covered a total of 13 8/10 miles while driving to the museum and returning home.

Answer 2

13.8 miles

Explanation:

The driving distance from Alex's house to the museum is
`6(9)/(10)` miles

Since the distance from his house to the museum does not change, his trip back is also
`6(9)/(10)` miles.

The Round-Trip Distance is the distance to and from the museum.

To determine this, there ate two approaches.

1. Add the distances together
2. Multiply the distance to by 2.

Approach 1

`6(9)/(10)+6(9)/(10)\\\\=(69)/(10) + (69)/(10) \\=(69+69)/(10)\\=(138)/(10)\\=13(4)/(5)=13.8`

Approach 2

`6(9)/(10) X 2 \\=(69)/(10) X 2\\=(69X2)/(10)\\=(138)/(10)\\=13.8 miles`

The round trip distance is 13.8 miles.