S3:E02 Finders Keepers

NUMB3RS - Season 3 - "Finders Keepers" - Barging In

Algebra 2 / Pre-CalculusActivity PDF
Step 1 of 5

Barging in on the Limits of Time

Before dive logs and fuel levels are checked, let's understand how far a barge can physically travel. Marine salvage barges are built for heavy lifting, not speed. A salvage barge has a typical maximum speed of about 15 knots (which is approximately 17 miles per hour).

If the barge traveled at its absolute maximum speed of 17 mph for the entire 16 hours it was out, it would cover a massive distance of 272 miles. However, Charlie calculated that the barge traveled no more than 20 miles. Let's calculate the average speed of the barge based on Charlie's 20 miles limit.

Question

If the barge was out for 16 hours and traveled a maximum distance of 20 miles as Charlie estimated, what was its average speed in miles per hour (mph)?

Hint: Use the formula Average Speed = Distance / Time.

Search Radius Visualization

Calculated based on joint variation formulas

Radius: 22.67 miles
15 mi30 miSouthNorthDOCK (Origin)

Interactive Parameter Controls

Barge Weight(ww)
1500 tons
More weight decreases total potential distance (inverse variation).
Fuel Consumed(ff)
68 gallons
More fuel allows for greater distance (direct variation).
Variation Constant(kk)
500 ton-miles/gal
Specifies fuel efficiency rating of the barge's diesel engine.

Efficiency Ratio (Decimal Format):

Fuel efficiency performance modifier: 0.85
Search space optimization index: 0.12