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

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?

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.