Time Speed Distance – Tricky yet simple question

Try this question:

Bill travels from point A to point B at a constant speed of 120 kilometers per hour. Upon reaching point B, he immediately heads back to point A. On his return trip to point A, Bill spends half the time traveling 20 kilometers per hour, and half the time traveling 60 kilometers per hour. What is Bill’s average speed, in kilometers per hour, for the entire roundtrip? A) 48 B) 60 C) 66 2/3 D) 72 E) 80

Method 1 Long cut

Let D = distance from A to B Given that Distance = Rate x Time, let T1 = D1/20 equal time spent travelling 20 kph. Similarly, let T2 = (D-D1)/60 equal time spent travelling 60 kph Since these times are equal, D1/20 = (D-D1)/60. Solving for D1 = D/4. Therefore, distance travelled at 60 kph = D-D/4 or 3D/4 Time spent on trip from A to B = D/120. Time spent travelling 20 kph = (D/4)/20 = D/80. Note that time spent travelling 60 kph is given to be the same, also D/80. Average speed = total distance travelled/total time = 2D/[(D/120 + (D/80)+(D/80)] Notice the D’s cancel in numerator and denominator. Common denominator is 240, so: 2/[(2/240)+(3/240)+(3/240)] = 2/(8/240) = 240/4 = 60

Method 2 – Shortcut

Because on the return trip we spend an equal amount of time traveling at 20mph and 60mph, the average speed for the return trip is 40mph. Now pick a simple number for the distance. Say we go 120 miles.The trip there will take 1 hour at 120mph. The trip back will take 3 hours at 40mph. Total time = 1 + 3 = 4 hours Total distance = 120 + 120 = 240 miles Average speed for trip = 240/4 = 60mph, or option B. time speed and distance questions and answers time and distance problems tricks pdf time speed and distance shortcuts pdf time and distance shortcuts tricks time speed and distance tricks for cat time and distance problems with solutions pdf for bank exams time and distance concepts time and distance tricks