Time, Work and Distance

Overview

Time, Work and Distance is one of the most application-oriented topics in the MP TET Mathematics section. These problems test a candidate's ability to apply arithmetic reasoning to real-life situations—workers completing tasks, taps filling tanks, vehicles covering distances, and boats moving in streams. The topic draws heavily on concepts of ratio, proportion, and the unitary method.

For MP TET, expect 2–4 questions from this combined topic across Varg-1, Varg-2, and Varg-3 papers. Questions range from straightforward calculations to multi-step word problems. Mastery requires understanding the underlying relationships (work ∝ 1/time, distance = speed × time) and developing the ability to quickly set up equations from worded scenarios.

The key to success is recognising problem types instantly and applying the correct formula without confusion. Most errors stem from mixing up concepts or misreading the question—skills that improve with systematic practice.

---

Key Concepts

• **Work and Time are inversely related**: If A completes a job in 10 days, A's one day work = 1/10. More efficient workers take less time.

• **Combined Work**: When A and B work together, their combined one day work = (1/a) + (1/b), where a and b are their individual completion times.

• **Efficiency Ratio**: If A is twice as efficient as B, then A takes half the time B takes. Efficiency ∝ 1/Time.

• **Distance-Speed-Time Triangle**: Distance = Speed × Time. Rearrange as needed: Speed = Distance/Time, Time = Distance/Speed.

• **Relative Speed**: When two objects move in the same direction, relative speed = difference of speeds. When moving towards each other, relative speed = sum of speeds.

• **Average Speed**: For a journey with two different speeds, Average Speed = (2 × S₁ × S₂)/(S₁ + S₂) when distances are equal. Do NOT simply average the speeds.

• **Upstream and Downstream (Boats/Streams)**: Downstream speed = Boat speed + Stream speed. Upstream speed = Boat speed − Stream speed.

• **Pipes and Cisterns**: Inlet pipes do positive work (fill); outlet pipes do negative work (empty). Combine as algebraic sum.

---

Formulas / Key Facts

| Concept | Formula | |---------|---------| | One day's work | If total work done in n days, one day work = 1/n | | Combined work (A and B together) | 1/T = 1/a + 1/b, so T = (a × b)/(a + b) | | Work with efficiency | Work = Efficiency × Time | | Distance formula | D = S × T | | Relative speed (same direction) | S_rel = S₁ − S₂ | | Relative speed (opposite direction) | S_rel = S₁ + S₂ | | Average speed (equal distances) | S_avg = 2S₁S₂/(S₁ + S₂) | | Downstream speed | S_down = B + R (B = boat, R = river/stream) | | Upstream speed | S_up = B − R | | Speed of boat in still water | B = (S_down + S_up)/2 | | Speed of stream | R = (S_down − S_up)/2 |