Question

Both Allison and Jennifer jogged on sunday. when asked about their distances, Allison said, " i ran 2 7/8 miles this morning and 3 3/8 miles this afternoon. So, i ran a total of about 6 miles, " and Jennifer said, "i ran 3 1/10 miles this morning and 3 3/10 miles this evening. i ran a total of 6 4/10 miles."How do their answers differ? explain why they are both correct.

Answer 1

1. Their answers differ because of approximation

2. See Explanation Below

Explanation:

Given

Allison

`Morning: 2(7)/(8) miles`

`Afternoon: 3(3)/(8) miles`

Total: About 6 miles

Jennifer

`Morning: 3(1)/(10) miles`

`Afternoon: 3(3)/(10) miles`

Total:
`6(4)/(10) miles`

Required

1. How their answers differ
2. Why they are both correct

How their answers differ

To understand how their answers differ; first we need to calculate the actual miles they both ran.

Total = Distance covered in the morning + Distance covered in the evening

For Allison

Total Distance =
`2(7)/(8) + 3(3)/(8)`

Convert mixed fractions to improper fractions

Total Distance =
`(23)/(8) + (27)/(8)`

Take LCM and add

Total Distance =
`(23 + 27)/(8)`

Total Distance =
`(50)/(8)`

Total Distance = 6.25 miles

For Jennifer

Total Distance =
`3(1)/(10) + 3(3)/(10)`

Convert mixed fractions to improper fractions

Total Distance =
`(31)/(10) + (33)/(10)`

Take LCM and add

Total Distance =
`(31 + 33)/(10)`

Total Distance =
`(64)/(10)`

Convert to improper fraction

Total Distance =
`6(4)/(10) miles`

From the calculation above, the total distance ran by Allison is 6.25 miles and she said she ran about 6 miles; This means that she approximated the total distance she covered.

Also from the calculation above, the total distance ran by Jennifer is
`6(4)/(10) miles` and she said she ran
`6(4)/(10) miles`; This means that she gave the actual distance she ran.

Hence, their answers differ because of approximation

Why they are both correct?

As mentioned above, the difference in their answer is approximation.

Approximation is rightly allowed in measurements as long as one is giving the right approximated value.

For Allison; the approximation of 6.25 miles is 6 miles;

For Jennifer; she gave the actual distance she ran (
`6(4)/(10) miles`)

Base on this, we can conclude that both are correct