A fruit delivery truck traveled 65 miles for Monday deliveries. The truck starts at the fruit distribution center, makes 3 deliveries, and returns to the fruit distribution center. The four distances traveled are consecutive numbers that differ by half a mile. How far is it from the Fruit distribution center to his first delivery?

A) 15.5 miles

B) 16

C) 16.5

D) 17

Let x be the distance from the Fruit Distribution center to his first delivery, then:

x+0.5 - - > second distance

x+0.5+0.5 = x+1 - - > third distance

x+1+0.5 = x+1.5 - - > fourth distance

x + x+0.5 + x+1 + x+1.5 = 65

4x + 3 = 65

4x = 65 - 3

4x = 62

x = 62/4

x = 15.5

The distance from the Fruit Distribution center to his first delivery is 15.5 miles.

So we know the total distance is 65 miles.

Let d1 = distance to 1st delivery from distribution center

d2 = distance to 2nd delivery from 1st delivery site

d3 = distance to 3rd delivery from 2nd delivery site

d4 = distance from 3rd delivery site back to distribution center.

So total distance D = d1 + d2 + d3 + d4 = 65

We know that d1 to d2, d2 to d3 and d3 to d4 each differ by 1/2 a mile.

This means that

d2 = d1 + 1/2

d3 = d2 + 1/2 = (d1 + 1/2) + 1/2 = d1 + 1

d4 = d3 + 1/2 = d1 + 1 + 1/2 = d1 + 3/2

Adding all these distances:

d1 + d2 + d3 + d4

= d1 + (d1 + 1/2) + (d1 + 1) + (d1 + 3/2)

= 4d1 + 3 = 65

d1 = (65 - 3) / 4

So the distance to the first delivery, d1 is (65 - 3) / 4.

Does that make sense?