Question

A student solved this problem and said the answer was 5 1 4 14 miles. Danielle ran 3 1 8 18 miles on Tuesday, 4 1 2 12 miles on Wednesday, and 5 1 4 14 miles on Thursday. How far did Danielle run altogether? Is the student's answer reasonable? No, the answer is not reasonable. It should be about 13 miles. Yes, the answer is reasonable. No, the answer is not reasonable. It should be about 2 miles. No, the answer is not reasonable. It should be about 20 miles.

Answer 1

Question

A student solved this problem and said the answer was
`5(1)/(4)` miles. Danielle ran
`3(1)/(8)` miles on Tuesday,
`4(1)/(2)` miles on Wednesday, and
`5(1)/(4)` miles on Thursday. How far did Danielle run altogether? Is the student's answer reasonable?

- No, the answer is not reasonable. It should be about 13 miles.

- Yes, the answer is reasonable.

- No, the answer is not reasonable. It should be about 2 miles.

- No, the answer is not reasonable. It should be about 20 miles.

Answer:

- No, the answer is not reasonable. It should be about 13 miles.

Explanation:

Given

Student solution =
`5(1)/(4)` miles.

Miles covered on Tuesday =
`3(1)/(8)` miles

Miles covered on Wednesday =
`4(1)/(2)` miles

Miles covered on Thursday =
`5(1)/(4)` miles

Required

- Total distance covered by the student

- Is the student answer reasonable?

To calculate the actual distance covered by Danielle, we simply add the distance covered on each day,

This goes thus

Distance =
`3(1)/(8)` +
`4(1)/(2)` +
`5(1)/(4)`

Convert to Improper Fractions

Distance =
`(25)/(8)` +
`(9)/(2)` +
`(21)/(4)`

Take LCM

Distance =
`(25 + 36 + 42)/(8)`

Distance =
`(103)/(8)`

Distance = 12.875

From the calculations above, we can conclude that the student's answe is not reasonable because his calculation (
`5(1)/(4)` miles) is much more smaller than the actual result 12.875 miles

From option A through D, Only option A is correct because 12.875 miles cam be approximated to 13 miles.

Hence,

A. - No, the answer is not reasonable. It should be about 13 miles.

is the right answer