3:24
Rates: work problems
Two Painters, One Room
Alice can paint a room in 6 hours. Bob can paint the same room in 3 hours. Working together, how long will it take them to paint the room?
Concepts
Concept demo
Concepts
Featured · MCAT fluids: Poiseuille's law
A plaque halves the radius of a coronary artery. A three-minute film on why the blood flow does not halve, or quarter, but falls to one sixteenth, and why that fourth power runs the circulation.
Pause, scrub, read alongEvery frame is computed
Pick up where you left off
Five SAT problems and one from the MCAT, each built around a real test question: the traps, the one picture that makes the idea obvious, the general rule. Every film has an interactive version where the numbers change and the set redraws itself.
3:24
Rates: work problems
Alice can paint a room in 6 hours. Bob can paint the same room in 3 hours. Working together, how long will it take them to paint the room?
3:21
MCAT fluids: Poiseuille's law
A plaque narrows a coronary artery to half its original radius. If the pressure difference across the segment and the viscosity of the blood are unchanged, blood flow through the segment falls to what fraction of its original value?
4:26
Systems of linear equations: distance, rate and time
A freight train leaves a station heading east at 40 miles per hour. Two hours later an express train leaves the same station on a parallel track heading east at 60 miles per hour. How many hours after the express leaves does it catch the freight train?
4:05
Average speed: total distance over total time
A cyclist rides from her house to the beach at 20 miles per hour and rides back along the same road at 30 miles per hour. What is her average speed for the whole round trip?
4:06
Circles: completing the square
In the xy-plane, the graph of x² + y² + 6x − 4y = 12 is a circle. What is the radius of the circle?
3:50
Similar triangles: proportions
At a certain time of day, a flagpole casts a shadow 36 feet long. At the same time, a person 5 feet tall standing nearby casts a shadow 4 feet long. How tall is the flagpole?
Five rounds each: sliders, multiple choice and a trap round, with the set showing the truth after every answer. A sandbox tab lets you change the numbers freely. Scores are remembered in this browser.
Two Painters, One RoomRates
5 rounds · sandbox
Not started
Practice
The Narrowed ArteryPoiseuille
5 rounds · sandbox
Not started
Practice
Two TrainsSystems
5 rounds · sandbox
Not started
Practice
The Round TripAverage speed
5 rounds · sandbox
Not started
Practice
The Unfinished SquareCircles
5 rounds · sandbox
Not started
Practice
The ShadowSimilar triangles
5 rounds · sandbox
Not started
Practice
Every frame is a function of the clock, so a film can be paused, scrubbed, re-timed to a new narrator, or re-rendered with different numbers. The same engine drives the film and the practice set.
Each film follows the shape of a good tutor's explanation: state the question, show why the tempting answers fail on the set itself, then let one camera move carry the argument.
A tutor beside the set: ask "what if Bob were slower?" and watch the room answer. The practice engine already takes the numbers; the conversation is the layer on top.