Question

The temperature fell from 0 Degrees Fahrenheit to 15 and one-half Degrees Fahrenheit below 0 in 5 and three-fourths hours. Wen tried to find the change in temperature per hour. Her work is shown below. Negative 15 and one-half divided by 5 and three-fourths = negative StartFraction 31 over 2 EndFraction divided by StartFraction 23 over 4 EndFraction = negative StartFraction 31 over 2 EndFraction times StartFraction 23 over 4 EndFraction = Negative StartFraction 713 over 8 EndFraction

Answer 1

C. Wen did not take the reciprocal of the divisor

Explanation:

Answer 2

The correct answer will be:

`-(62)/(23)`

Explanation:

It is given that :

Initial temperature,
`T_1 = 0^\circ F`

Final temperature,

`T_2 = -15(1)/(2)^\circ F\\\Rightarrow T_2 = -(15* 2+1)/(2) ^\circ F\\\Rightarrow T_2 = -(31)/(2) ^\circ F`

Time taken :

`5(3)/(4)\ hrs = (5 * 4+3)/(4)\ hrs = (23)/(4)\ hrs`

Change in temperature per hour:

`\frac{\text{Difference of temperature}}{\text{Total Time Taken}}\\\Rightarrow \frac{T_2-T_1}{\text{Total Time Taken}}`

Putting the values of temperatures and time:

`((-31)/(2)-0)/((23)/(4))\\\Rightarrow ((-31)/(2))/((23)/(4))\\\Rightarrow (-31 * 4)/(2 * 23)} \text{---- Error done by Wen at this step}\\\Rightarrow (-31 * 2)/(23)}\\\Rightarrow (-62)/(23)}`

The error done by Wen was during calculating the values of fraction.

So, the correct answer is :
`(-62)/(23)}` instead of
`(-713)/(8)`