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Problem 5

# Jacob drove $$15 \frac{1}{2}$$ miles a day for 6 days in a row. How many miles would he have to drive a day to cover the same distance in $$\frac{1}{3}$$ the number of days?

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#Step 1: Calculate total miles driven by Jacob during the 6 days# $Total\, Miles = 15.5\, miles/day \times 6\,days = 93\,miles$ #Step 2: Compute 1/3 of the number of days# $Fewer\, Days = \frac{1}{3} \times 6\,days = 2\,days$ #Step 3: Calculate miles to be driven daily in fewer days# $Miles\, per\, Day = \frac{Total\, Miles}{Fewer\, Days} = \frac{93\,miles}{2\,days} = 46.5\,miles/day$ So, Jacob would have to drive $$46.5$$ miles a day to cover the same distance in $$\frac{1}{3}$$ the number of days.
See the step by step solution

## Step 1: Calculate total miles driven by Jacob during the 6 days

To find the total miles driven during these six days, we can multiply the daily distance by the number of days: $Total\, Miles = 15.5\, miles/day \times 6\,days$

## Step 2: Compute 1/3 of the number of days

Now, we need to calculate the fewer days, which is $$\frac{1}{3}$$ of the total days. $Fewer\, Days = \frac{1}{3} \times 6\,days$

## Step 3: Calculate miles to be driven daily in fewer days

To compute the miles he needs to drive per day in fewer days, divide the total miles by the fewer days from Step 2: $Miles\, per\, Day = \frac{Total\, Miles}{Fewer\, Days}$ Let's now compute the results for each step.

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