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U-Haul Moving

This Problem Based Learning Unit involves developing a mathematical model to determine what size U-

Haul truck the facilitator should rent to move his/her belongings from one house to another.

Concepts taught:

Linear Functions

Multiple representation

Entry Event

Facilitator : Great news everybody. Principal ________ gave me a huge raise. It turns out that, contrary

to all the media reports, the school district is flush with cash. As such, Im moving on up. To the East side.

I bought a MTV-cribs-like house. Unfortunately, I dont have my hands on the huge sums of money yet,

so Ill be using a U-Haul to transport my currently meager possessions. Heres a map of my old house,

new house, and U-Haul rental location.

[Facilitator shows slide / handout of map]

Facilitator: Now, the local U-Haul rental has different fees for different sized trucks. The larger the

moving truck, the more it costs. Here is their pricing scheme.

8/7/2019 Uhaul PrBL


[Facilitator shows slide / handout of U-Haul pricing table. Note: alternatively, the facilitator could direct

them to the U-Haul website to obtain the specs: 14 truck, 17 truck, 20 truck]

Truck length U-Haul listed capacity Up front cost (1 day

rental)

Additional cost per

mile

14 733 cu. Ft. $19.95 $0.7917 865 cu. Ft. $29.95 $0.79

20 1015 cu. Ft. $39.95 $0.79

Facilitator: Now, Im not exactly sure how much stuff I have. It might take 1 trip with these trucks, it

might take 10. So Im going to go calculate my furniture while you guys help me come up with a

mathematical model, suggesting which truck I should get depending on the number of trips I have to

take.

Potential solution:

First students will have to determine a distance to and from each location on the map.

From U-Haul rental to Old Home: ~3 mi

From Old Home to New Home: ~7 mi

From New Home to U-Haul Rental: ~4 mi

Students then will need to set up a model in the form of a linear function, depending on the number of

trips between the Old Home and New Home. Each extra trip after the first one will tack on 14 miles to

the total mileage.

Cost = (Up front cost of truck)+$0.79*(mileage from U-Haul to Old Home + mileage between Old Home

and New Home + mileage from New Home to U-Haul) + $0.79*2*(mileage from Old Home to New

Home)*(number of trips - 1)

Cost = (Up front cost of truck)+$0.79*(3 + 4) + $0.79*2*(7)*(number of trips -1)

Cost = (Up front cost of truck)+$0.79*(7) + $0.79*2*(7)*(number of trips - 1)

Cost = (Up front cost of truck)+$5.53+$11.06*(number of trips - 1)

We can break that down for the three given truck sizes. For the smallest truck (the 14 truck):

where x = # of trips to and from the New/Old Home

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For the other two trucks:

Using a table:

# of

trips:

1 2 3 4 5 6 7 8 9 10

14

truck

25.48 36.54 47.6 58.66 69.72 80.78 91.84 102.9 113.96 125.02

17

truck

35.48 46.54 57.6 68.66 79.72 90.78 101.84 112.9 123.96 135.02

20

truck

45.48 56.54 67.6 78.66 89.72 100.78 111.84 122.9 133.96 145.02

Entry Event #2

Facilitator: Im still working on figuring out the number of trips Ill have to take. I had several moving

companies come over before I decided to rent a U-Haul and they each gave me a wildly different

estimate of the amount of cubic footage of stuff I have.

Estimate 1: 2225 cu. ft

Estimate 2: 2891 cu. Ft.

Estimate 3: 3262 cu ft.

Estimate 4: 4022 cu ft.

Which size truck should I rent, based on each estimate?

Potential solution.

Each estimate would entail a different number of trips based on the size of the truck rented. Recall,

Truck length U-Haul listed capacity

14 733 cu. Ft.

17 865 cu. Ft.

20 1015 cu. Ft.

Truck

capacity

14 truck (733

cu ft)

17 truck (865

cu ft)

20 truck

(1015 cu ft)

Estimate 1:

2025

3 trips 3 trips 2 trips

Estimate 2: 4 trips 4 trips 3 trips

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2891

Estimate 3:

3462


Estimate 4:

4511


We can translate this into cost also using a table. (most cost effective)

Cost using 14'

truck

Cost using 17'

truck

Cost using 20'

truck

Estimate 1 47.6 57.6 56.54

Estimate 2 58.66 68.66 67.6

Estimate 3 69.72 79.72 78.66

Estimate 4 91.84 90.78 89.72

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