Time-Work, Speed-Distance, and Trains

Rate Is the Common Idea

Time and work, pipes, speed-distance, boats, and trains look different, but they share one idea: rate. A worker completes work per day. A pipe fills a tank per hour. A train covers metres per second. A boat moves relative to water. Once the rate is clear, the formula is simple.

The official syllabus separately names Time and Work and Time and Distance. RRB NTPC questions usually stay arithmetic, but they mix units and wording. The candidate who writes the rate first avoids most traps.

Core Formulas

Time and Work

If A can finish a job in 12 days, A does 1/12 of the job per day. If B can finish it in 18 days, B does 1/18 per day. Together they do 1/12 + 1/18 per day. Add the rates, then invert to get time.

The LCM method is often faster. Take total work as the LCM of the days. For 12 and 18 days, total work can be 36 units. A does 3 units per day, B does 2 units per day, together 5 units per day. Time is 36/5 days. This avoids fraction errors.

For efficiency problems, if a worker is twice as efficient, the worker takes half the time. If wages are divided by work done, use efficiency or units completed, not days spent alone.

Pipes and Cisterns

A filling pipe has positive work. An emptying pipe has negative work. If one pipe fills a tank in 6 hours and a leak empties it in 12 hours, net rate is 1/6 - 1/12 = 1/12 tank per hour. The tank fills in 12 hours.

Label every pipe before adding. Many candidates add an emptying pipe by mistake. If the tank is filling despite a leak, the combined rate must still be positive. If the leak is faster than the inlet, the tank cannot fill under those conditions.

Speed, Distance, and Time

Speed problems become easy when units match. If speed is in km/h and distance is in metres, convert before using the formula. For train and pole problems, metres per second is usually the natural unit.

Average speed is not always the average of speeds. If equal distances are travelled at two speeds a and b, average speed is 2ab/(a+b). If equal times are spent at two speeds, the average is the simple average. The difference is important in journey questions.

Use a quick reasonableness check. If a vehicle covers 180 km at 60 km/h, time is 3 hours. If your answer is 30 hours or 30 minutes, a unit mistake is likely.

Relative Speed

When two objects move in the same direction, subtract speeds. When they move in opposite directions or towards each other, add speeds. Relative speed is the rate at which the gap changes.

This applies to trains, people walking, and boats in current. In boats, downstream speed is boat speed in still water plus stream speed. Upstream speed is boat speed minus stream speed. From downstream and upstream speeds, still-water speed is their average, and stream speed is half their difference.

Train Problems

A train crossing a pole covers its own length. A train crossing a platform covers train length plus platform length. Two trains crossing each other cover the sum of their lengths. The time formula remains distance divided by relative speed.

Train Distance Guide

Always convert train speed to m/s when lengths are in metres. If two trains have speeds in km/h, first find relative speed in km/h, then convert to m/s. This is cleaner than converting each separately, though both methods work.

Exam Strategy

Write units beside numbers in rough work. Mark workers as rates, speeds as distance per time, and pipes as positive or negative. Use LCM for work and metres per second for trains. These habits reduce calculation load.

Under CBT pressure, do not spend too long on a complex work-chain problem in the first pass. Secure direct rate questions first. Return to multi-step cases after finishing easier arithmetic.

If a problem gives many people, days, and efficiency changes, reduce it to total work units before touching the options. If a speed problem gives a stoppage or delay, separate running time from waiting time. This prevents a common mistake: treating total journey time as moving time.

Practice Plan

Build mixed sets: five work questions, five pipe questions, five speed questions, five train questions, and five relative-speed questions. After each set, classify mistakes as unit, sign, distance choice, inverse relation, or arithmetic. Most improvement comes from fixing the repeated category, not from solving hundreds of similar questions blindly.