Time Speed Distance Questions and Answers

Time, Speed, and Distance (TSD): Speed = Distance / Time, Distance = Speed x Time, Time = Distance / Speed. Unit conversions: km/hr to m/s = multiply by 5/18; m/s to km/hr = multiply by 18/5. If two objects travel the same distance at speeds S1 and S2, ratio of times = S2:S1 (inverse). TSD problems appear in SSC CGL, IBPS Bank PO, SBI PO, Railway, and CAT exams.

Average Speed when same distance: Average Speed = 2ab/(a+b) where a and b are the two speeds. Do NOT use (a+b)/2. Example: Going at 40 km/h and returning at 60 km/h, average speed = 2x40x60/(40+60) = 4800/100 = 48 km/h. Average Speed when same time: Average Speed = (a+b)/2. For three speeds over equal distances: Average = 3abc/(ab+bc+ca).

Train Problems: Two trains passing in same direction, relative speed = difference of speeds. Going opposite direction, relative speed = sum of speeds. Time to pass = (Sum of lengths) / Relative speed. Time for train to pass a stationary object = Length of train / Speed. Time to cross a platform = (Length of train + Length of platform) / Speed of train. These problems are very common in Railway and SSC exams.

Boat and Stream: Upstream speed = Boat speed - Stream speed. Downstream speed = Boat speed + Stream speed. Boat speed = (Downstream + Upstream speed) / 2. Stream speed = (Downstream - Upstream speed) / 2. Time upstream = D/(u-v), time downstream = D/(u+v) where u = boat speed and v = stream speed. These problems are standard in IBPS, SBI, and SSC competitive exams.

Relative Speed: Two people starting from same point in same direction at speeds a and b (a>b), relative speed = a-b. Starting from opposite ends at speeds a and b, relative speed = a+b, time to meet = Distance/(a+b). Circular track: For two going same direction, time to meet = Circumference/(a-b). For opposite directions = Circumference/(a+b). After meeting, ratio of remaining distances = a:b.