Time, Speed & Distance - Soumya Chakraborty

  • IIM Lucknow | MathOratory

    Request you to start solving without variables... variables make you slow!

    Mr. Ghosh arrives at his office 30 min late every day. On a particular day, he reduces his speed by 25% and hence arrived 50 minute late instead.
    (1) Find how much time would he take to travel to his office if he decides to be on time on a blue moon day?
    (2) If he has to arrive on time, by what percentage should he increase his speed? (Assume on each of these days, he starts from his home at the same time)

    As he is reducing his speed by 25%, the speed becomes 75% or 3/4
    So time should become 4/3, or increases by 1/3... So that 1/3 increase corresponds to an increase of 20 mins (30 to 50 mins late)
    Thus time taken to travel in the previous speed is 20*3 = 60 mins...
    Now as he reaches 30 mins late, he needs to drop his total time by 30 mins to reach on time, or he needs to reach in 60 - 30 = 30 mins (answer to the first part)
    Now, instead of reaching in 60 mins, he has to reach in 30 mins. Or, he has to half his time and in order to halve the time, one would need to double the speed... Or in other words, increase the speed by 100%

    A train after reaching exactly halfway to a platform that is double its own length, takes 40 s to cross the platform completely. How long will the train take to completely cross a bridge that is exactly 5 times the length of the platform ?

    If 2 is 40
    Then 11 is 220
    That's it right!

    A boy can reach his school 20 minutes early if he increase his speed by 25%. How much time does he take to reach his school, travelling at his usual speed?

    Correct answer 100 mins

    Two cars start from point A at the same time every day, travelling towards point B via the same path. The faster car reaches point B 15 seconds earlier than the slower car. One day, the slower car starts 10 seconds early. the faster car, starting at the usual time, doubles its usual speed. The faster car again reaches 15 seconds earlier than the slower car. Find the speed ratio of the faster car to the slower car.

    Correct answer 7:4

    A man picks up his child from school at 4 P every day. He reaches 4 PM sharp and wastes no time waiting for his child and immediately turns back and returns home. One day, the school gets over by 12 PM, which the main in unaware of. The child, instead of waiting for the father, starts walking towards his home after the school gets over. The father picks up his child somewhere in between his home and the school and manages to reach home 1.5 hours early. Find the ratio of the Father's driving speed and the child's walking speed.

    It is because the father picks the child somewhere in between, they save the 1.5 hours. The father actually saves the time to travel from the point he picks up the child to the school and also back to that point from the school. So, the father must take 45 mins to travel one way from that point to the school. And as we know the father reaches school exactly at 4:00 pm, he must have been at that point at 3:15.
    Which also implies, the child has been walking for 3 hours 15 mins, viz 195 mins.
    So the same distance with the car's speed takes 45 mins and by the child's walking speed takes 195 mins to travel.
    Thus time ratio = 3:13
    Speed ratio = 13:3

    Two people A and B starts jogging every morning from points P and Q, not necessarily at the same time, travelling towards Q and P respectively. Every day they meet at a point R, somewhere between P and Q. Speed of A = 10 km/h and Speed of B = 20 km/h.
    a) One day, A starts 30 minutes later then the usual time. How much behind the point R, did A meet B?
    b) The next day, A was on time, however B started 30 minutes later than its usual time. How much further the usual meeting point R, did A meet B?

    Answer is 3.33 for both questions

    5 buses start at different times from Point A towards Point B. Their speeds are in the ratio 1:2:3:4:6. All bus reach point B at the same time. If the fastest bus starts 10 hours after the one which started 2nd from Point A, find the time taken for the bus which started after 2 buses from Point A.

    A person travelling in a moving train hears 2 gunshots at an interval of 15 seconds. If, however, the two shots were fired actually at an interval of 18 seconds, find the speed of the train (Assume speed of sound = 330 m/s)

    Detailed Video Solutions:

    If a boy walks to his school 2 km/h faster than his usual speed, he reaches 10 minutes early. If however, he walks with 2 km.h slower than his usual speed, he reaches 20 minutes late. Find the usual walking speed.

    This is a property of hm
    If the hm of a and b is 'h'
    Then the ratio of a:b is equal to the ratio of their differences from h
    That is a/b = (a-h) /(h-b)

    we know the ratio of speeds are 2:1 and their difference is 4
    so the speeds are 8 and 4
    usual speed is avg of these two = 6

    HM for two numbers

    HM = 2ab/(a + b)

    There is a faster method

    Find the HM of 30 and 50
    Step 1: Take the ratio = 3:5
    Step 2: Find the difference = 20
    Step 3: Divide the difference in the above ratio = 3/8 * 20 & 5/8 * 20
    HM = 30 + 3/8 * 20 = 37.5 or 50 - 3/8 * 20 = 37.5
    This results from the property:
    If HM(a,b) = h
    Then (a - h)/(h - b) = a/b

    A person is travelling from Point P to point Q at a constant speed. Buses with equal speeds leave points P and Q (towards Q and P respectively) at same intervals. If a bus which is travelling from P to Q crosses the person every 60 minutes and a bus which is travelling the other way meets the person every 40 minutes, find the interval at which the buses ply from either points.

    Details & Assumptions:

    • The interval at which buses start from either ends is same.
    • Buses MAY NOT start at the same time from point P and Q

    Ram was jogging towards beach one fine morning. He was travelling with a speed of 12 km/h. The distance to the beach was 24 km. There was a dog with Ram, who started running to and from between Ram and the beach till Ram reached the beach.
    (1) What was the total distance run by the dog?
    (2) What was the sum of distances run by the dig in the direction from Ram to the beach.

    Total Distance = 60 km
    Distance run towards the beach = 42 km

    A and B start from points P and Q travelling towards Q and P, respectively. If A takes 60 minutes to travel the entire distance and B takes 84 minutes to do the same, after how long did they meet?
    (a) 30 minutes
    (b) 32 minutes
    (c) 35 minutes
    (d) 40 minutes [CAT 2014]

    Answer is 35

    A dog is stuck inside a tunnel AB, at a point P, such that AB = 5AP. The dog hears a train approaching towards the tunnel and start running towards B and just manages to escape. If, however, the dog would've ran towards A, it would have still managed to escape. Find the ratio of speeds of the train and that of the dog.

    A vehicle travelling a certain distance, develops an engine trouble somewhere in between, thereby reducing the speed by 25%. Due to this, the vehicle reached the destination 50 minutes late. If, however, the engine trouble would've occurred 40 KM ahead, the would've reached the destination only half an hour late. Find the speed of the vehicle before the engine trouble. Also, find the sum of distances travelled by the vehicle in the two scenarios after the engine trouble occurred.

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