Rate and Total: Turn a Rate and a Time Into a Total, and Back

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Opens on Chapter 1’s example: 45 mph for 20 minutes; Nell’s phone going from 80% to 52% in 2 hours; a 40-gallon bath; two savings jars.

1. A steady rate

Rate, per hour mph, gallons an hour…

For how many minutes

2. A rate from two readings

First reading a battery %

Later reading

Hours between

Time until it reaches

3. A rate that changes partway

Total to fill gallons

First rate per minute

For minutes

Then a rate of per minute

4. A steady amount against a growing one

Each week (steady) $

The other grows by $ a week

Weeks

Enter your numbers, then press Work it out.

How it works

A rate times a time gives a total: miles per hour × hours = miles, gallons per minute × minutes = gallons. Watch the units: 20 minutes is 20/60 of an hour. A rate from two readings is the change divided by the time between them, and a forecast from it is a straight line drawn forward, true only if the rate holds. When the rate changes partway, work each stretch on its own and add them. On a graph of rate against time, each stretch is a rectangle and the total is its area: the idea Part Four builds on.

From the book, Chapter 1. 45 mph for 20 minutes is 15 miles. The phone drops 28 points in 2 hours, 14 an hour, so the last 32 points to 20% take about 2 hours 17 minutes. The 40-gallon bath takes 10 minutes at 4 a minute, or 15 if the tap drops to 2 after 5 minutes. The steady jar reaches $50 in ten weeks; the growing one $95. Every chapter and its calculator →

Numbers can be typed as 1,450, $38, 0.40, 12%, 1/6 or 2 3/8. Functions can be typed as 16t², 6 + 48t − 16t^2, 1000e^(0.05t) or √x; answers are rounded half up, the way the book rounds. Everything stays in your browser: no sign-up, nothing stored or sent.