Time & Work, Time, Speed & Distance
Time-and-work and time-speed-distance look like two topics but share one idea: work rate. If a job takes 6 days, the rate is 1/6 of the job per day — and rates simply add. Turning every question into rates first is what makes this chapter fast.
Don't read this page — work through it. Each block asks you to commit to an answer before it tells you anything.
Start here: what do you already know?
Time, work, speed — true or false?
6 statements · 12s each
Everything as a rate
| Situation | Rate |
|---|---|
| A alone takes 12 days | 1/12 per day |
| B alone takes 18 days | 1/18 per day |
| A and B together | 1/12 + 1/18 = 5/36 per day |
| Time together | 36/5 = 7.2 days |
The shortcut for two workers: together they take (a × b) / (a + b) days. For 12 and 18, that is 216/30 = 7.2 — the same answer in one step.
Sort by which speeds combine
Add the speeds or subtract them?
0/6Two trains approaching each other
Which group does it belong to?
Commit to the answer
Compute, then check
1/4A does a job in 12 days and B in 12 days. Working together, how many days do they take?
7
Method, in order
Match the situation to its rule
Quick reference
Exam tip: never add or subtract times. Convert to rates, combine the rates, then invert at the end. Almost every wrong answer in time-and-work comes from adding days directly.