Lucia has collected a set of data and calculated the mode to be 31. the set contains 87 numbers, but lucia gets an email telling her to add the following 6 numbers to her data: {23, 26, 28, 30, 31, 40}

The problem seems to be lacking a question. But looking for the same problem from another source, we're looking for the new mode after adding the 6 numbers into the data set. 

Mode, in its most basic definition, is the number or data that is most repeated in a data set. For example, in {1, 1, 1, 2, 2, 3}, the most repeated number is 1. Hence, the mode is 1. 

Now, going back to Lucia's problem. Prior to adding the 6 numbers, the mode of the set of 87 numbers is already 31. That means 31 is the most repeated number in the set. Checking the numbers that were added, since another count for 31 is to be added, even if the number of 23, 26, 28, and 40 are increased by 1. 31 will still be the most repeated number in the set. Hence, the mode is still 31.

31

the distance between the school and her home is 3.6km.

explanation

12 mins = 0.2 hours = 1/5 hour

54 ÷ 3 = 18km per hour

1/5 of 18 = 3.6km per 12 mins