March 2020
Problem of the Month

Food Bank Truck

The Larimer County Food Bank Truck delivers the weekly food to McBackpacks in Fort Collins every Tuesday.   It was agreed that the truck should arrive exactly at 1:00 PM.

If the truck traveled at 40 mph it would arrive in Fort Collins at noon, an hour early.
If the truck traveled at 20 mph it would arrive at 2:00 PM, an hour late.

How far is the Food Bank from Fort Collins and how fast should it travel in order to arrive at 1:00 PM?

Click here to learn more about the McBackpack program in Fort Collins, Colorado

Solution to the Problem:

The Food Bank is 80 miles from Fort Collins and the truck would have to travel at 26.67 mph in order to arrive at 1:00 PM.

Let x = number of hours for the truck to arrive at 1:00 PM.
Then set up a rate/time/distance table:

	Rate	Time	Distance
Early	40	x - 1	40 (x - 1)
Late	20	x + 1	20 (x + 1)

Then 40x - 40 = 20x + 20
So, 20x = 60
x = 3 hours.

So the truck must travel 80 miles in 3 hours.
So the truck must travel 80 / 3 = 26.67 mph.

Correctly solved by:

1. Briggin Bluemel	Mountain View High School, Mountain View, Wyoming
2. James Alarie	Flint, Michigan
3. Ivy Joseph	Pune, Maharashtra, India
4. Brijesh Dave	Mumbai City, Maharashtra, India
5. Kelly Stubblefield	Mobile, Alabama
6. Anna T. Vice	Landon School, Bethesda, Maryland
7. Emre Karabiyik	Hacettepe University, Ankara, Turkey

Send any comments or questions to: David Pleacher