On a 1-mile walking tour of New York City, a group had to take a detour that was 300 yards shorter than half the distance of the tour. The detour is how many yards long?

580 yards long.

Step-by-step explanation:

The distance of the walking tour is = 1 mile

Step 1

We have to convert 1 mile to yards

Therefore,

1 mile = 1760 yards

Step 2

We are told that the group took a detour that was 300 yards shorter than half the distance of the tour.

The second step would be to find out how many yards is equal to half the distance of the tour.

Half the distance of the tour = 1/2 of a mile

And in step 1 we have converted whole distance of the tour to yards

= 1 mile = 1760 yards.

Hence, Half the distance of the tour = 1760 yards : 2

= 880 yards.

Step 3

The group took a detour that was 300 yards shorter than half the distance of the tour.

This means mathematically,

Half the distance of the tour - 300 yards

= 880 yards - 300 yards

= 580 yards.

Therefore, the detour was 580 yards long.