Question

Tim has an after-school delivery service that he provides for several small retailers in town. He uses his bicycle and charges $1.25 for a delivery made within 1 1/2 mi, $1.70 for a delivery of at least 1 1/2 mi but less than 1 3/4 mi, $2.15 for a delivery of at least 1 3/4 mi but less than 2 miles, and so on. If tim raised his rates by 10% what would he be paid to deliver a package 3 1/8 miles

Answer 1

$4.84

Explanation:

Given that

For delivery within
`1\frac{1}2` mi, charges = $1.25

For delivery within
`1\frac{1}2` mi -
`1\frac{3}4` mi, charges = $1.70

For delivery within
`1\frac{3}4` mi - 2 mi, charges = $2.15

and

so on.

i.e.

For delivery within 2 mi - 2
`\frac{1}4` mi, charges = $2.60

For delivery within 2
`\frac{1}4` mi - 2
`\frac{1}2` mi, charges = $3.05

For delivery within 2
`\frac{1}2` mi - 2
`\frac{3}4` mi, charges = $3.50

For delivery within 2
`\frac{3}4` mi - 3 mi, charges = $3.95

For delivery within 3 mi - 3
`\frac{1}4` mi, charges = $4.40

So, every 0.25 mi or
`\frac{1}4` mi increase in distance, there is an increase of $0.45 in the charges.

It is given that there is increase of 10% in the rates.

i.e. for every 0.25 mi increase in distance, there is an increase of 0.45*1.10 = $0.495 in the charges.

The distance of
`3\frac{1}8` miles lies within the range 3 mi - 3
`\frac{1}4` mi.

So actual charges after increase of 10%

`\Rightarrow \$4.40 * (110)/(100)\\\Rightarrow \$4.40 * 1.10\\\Rightarrow \bold{\$4.84}`