Question

Mr. Conners drove 78 1/3 miles on Monday, 77 1/12 on Tuesday, and 75 5/6 miles on Wednesday. If he continues this pattern on Thursday and Friday, how many fewer miles will he drive on Friday than on Tuesday?

a) 2 5/12 miles
b) 3 1/2 miles
c) 3 11/12 miles
d) 4 miles

Answer 1

After identifying the pattern of decreased mileage each day, by calculating the differences and converting to improper fractions, it was determined that Mr. Conners will drive 31/12 miles fewer on Friday than on Tuesday, which is 2 7/12 miles, none of the provided options exactly match the computed answer.

Step-by-step explanation:

To solve the problem of how many fewer miles Mr. Conners will drive on Friday compared to Tuesday, we need to understand the pattern of miles driven each day.

Mr. Conners drove the following miles:

• Monday: 78 1/3 miles
• Tuesday: 77 1/12 miles
• Wednesday: 75 5/6 miles

By examining the pattern, we find that each day Mr. Conners drives fewer miles than the previous day. On Tuesday, he drove 77 1/12 miles, which is 1 1/4 miles less than Monday (78 1/3 miles).

From Tuesday to Wednesday, the difference is:

77 1/12 - 75 5/6 = 1 1/4 + 1/12 = 1 1/3 miles less.

We can see that the amount by which the distance decreases each day consists of 1 mile and a fraction that increases by 1/12 each day:

1. From Monday to Tuesday: Decrease by 1 mile + 1/12
2. From Tuesday to Wednesday: Decrease by 1 mile + 2/12 (which is 1/4).

Hence, we can predict that:

• From Wednesday to Thursday: Decrease by 1 mile + 3/12 (which is 1/4).
• From Thursday to Friday: Decrease by 1 mile + 4/12 (which is 1/3).

Assuming the pattern continues, Mr. Conners will drive 1 1/3 miles fewer on Friday than he did on Thursday.

Since we are interested in how many fewer miles will be driven on Friday compared to Tuesday, we simply add up the daily decreases:

1 1/4 (Monday to Tuesday) + 1 1/3 (Wednesday to Thursday) + 1 1/3 (Thursday to Friday) =

1 1/4 + 1 1/3 + 1 1/3

Converting to improper fractions:

5/4 + 4/3 + 4/3 = 15/12 + 16/12 = 31/12 miles

Therefore, Mr. Conners will drive 31/12 miles fewer on Friday than on Tuesday, which is equivalent to 2 7/12 miles. The closest answer choice is:

a) 2 5/12 miles

However, there is no exact match in the provided options, so either there is a mistake in the options or in the calculation.