pAIrmatic Lessons

Distance, Rate, Time and Work

Grade 6 Grade 7

Arithmetic and pre-algebraOrder of Operations and Number Properties Divisibility Rules, Factors and Multiples Fractions and Decimals Integers and Absolute Value Percents and Consumer Math Ratios, Rates and VariationDistance, Rate, Time and WorkUnit Conversions

Distance, rate and time

Distance

d = r t

Rate

r = \frac{d}{t}

Time

t = \frac{d}{r}

Average speed

average speed = \frac{total distance}{total time}

Round trip at two speeds

v_{avg} = \frac{2 r_{1} r_{2}}{r_{1} + r_{2}}

equal distances each way

Work together

Combined work

\frac{1}{T} = \frac{1}{T_{1}} + \frac{1}{T_{2}}

T is the time working together

Time together

T = \frac{T_{1} T_{2}}{T_{1} + T_{2}}

Know the formula, still stuck?

Trouble with a formula often traces back to an earlier skill. Our free check-in finds the exact gap. A tutor then works on it with your child.

Find gaps free More practice