Malafola jogs 1/2 km on Monday, 1/2 km on Tuesday, and 3/4 km on Wednesday. What pattern can be used to…

Question

Malafola jogs 1/2 km on Monday, 1/2 km on Tuesday, and 3/4 km on Wednesday. What pattern can be used to predict the distance Malafola will jog on Thursday?

ScanSolve AI Tutor · Accepted Answer

Here's the solution to the problem:

Malafola's jogging distances are given for three days. We need to find the pattern to predict the distance for Thursday.

List the distances jogged and find the differences between consecutive days.
- Monday: $\frac{1}{2}$ km
- Tuesday: $\frac{1}{2}$ km
- Wednesday: $\frac{3}{4}$ km
Difference from Monday to Tuesday:
$\frac{1}{2} - \frac{1}{2} = 0 \text{ km}$
Difference from Tuesday to Wednesday:
$\frac{3}{4} - \frac{1}{2} = \frac{3}{4} - \frac{2}{4} = \frac{1}{4} \text{ km}$
Identify the pattern in the differences.
The difference in distance increased from 0 km (Monday to Tuesday) to $\frac{1}{4}$ km (Tuesday to Wednesday). This means the increase in distance itself is increasing by $\frac{1}{4}$ km each day.
Apply the pattern to find the distance for Thursday.
Following the pattern, the increase in distance from Wednesday to Thursday should be $\frac{1}{4}$ km more than the increase from Tuesday to Wednesday.
Increase for Wednesday to Thursday = (Increase from Tuesday to Wednesday) + $\frac{1}{4}$ km
Increase for Wednesday to Thursday = $\frac{1}{4} \text{ km} + \frac{1}{4} \text{ km} = \frac{2}{4} \text{ km} = \frac{1}{2} \text{ km}$

Now, add this increase to Wednesday's distance to find Thursday's distance:
$\text{Thursday's distance} = \text{Wednesday's distance} + \text{Increase}$ $\text{Thursday's distance} = \frac{3}{4} \text{ km} + \frac{1}{2} \text{ km}$ $\text{Thursday's distance} = \frac{3}{4} \text{ km} + \frac{2}{4} \text{ km}$ $\text{Thursday's distance} = \frac{5}{4} \text{ km}$ $\text{Thursday's distance} = 1\frac{1}{4} \text{ km}$
Malafola will jog $\boxed{\text{}\frac{5}{4} \text{ km or } 1\frac{1}{4} \text{ km}}$ on Thursday.

Malafola jogs 1/2 km on Monday, 1/2 km on Tuesday, and 3/4 km on Wednesday. What pattern can be used to predict the distance Malafola will jog on Thursday?

Answer

Step-by-step solution

List the distances jogged and find the differences between consecutive days.

Identify the pattern in the differences.

Apply the pattern to find the distance for Thursday.

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