HackerRank Time, Speed and Distance Quiz- 1

Let the length of the train be x metres.

Consider the length of man to be a point object comparison to length of train.

∴ Train covers x metres in 8 seconds

& (x+180) metres in 20 seconds.

Speed = distance/time

⇒ \frac{x}{8} = \frac{x+180}{20}\ \Leftrightarrow\ 20x=8(x+180)

∴ x= 120 m.

Speed of train = x/8 m/sec = 120/8 m/sec =15 m/sec.

When the trains run in opposite directions, we add their speed in order to find the relative speed.

∴ Relative speed= (45+36) kmph = 81 kmph

= 81 × 5/18= 22.5 m/sec.

Length of train= 22.5 × 8 = 180m.

Speed of Duronto = (150/15) m/s = 10 m/s

Speed of Antyodaya = (150/10) m/s = 15 m/s

∴ Relative speed= (10+15) m/s = 25 m/s

∴ Required time = (150+150)/25 m/s = 12 sec.

Speed of Himanshu from Bettiah to Motihari = 10 m/s = 36 km/h.

His speed on return trip= 150% of 36 = 54 km/h

Hence, average speed= \frac{2\times 36\times 54}{36+54}\ km/h = 43.2\ km/h

Ratio of speeds= 4:8:6 = 2:4:3

We know that, time= distance/speed.

i.e., time is inversely proportional to speed keeping distance constant.

∴ Ratio of time taken = (½) : (¼) : (⅓) = 6:3:4

Relative speed= (5-2) = 3 rounds per hour.

So, they cross each other 6 times in two hours and 1 time in half an hour.

Hence, they cross 7 times before 8:30 A.M.

Let, they meet x hours after 8 A.M.

Then, [distance moved by Akash in x hrs] + [distance moved by Janvi in (x-1) hrs]= 330

⇒ 60x + 75(x-1) = 330

∴ x= 3

So, they meet at (8+3) = 11 A.M.

Speed of ship= 5/3 m/s = 6 km/h

Speed upstream= (6-2) = 4 km/h

Speed downstream= (6+2)= 8 km/h

Distance travelled upstream = Distance travelled downstream = 40 km

∴ Total time taken = Time taken upstream + Time taken downstream

⇒ Total time taken = 40/4 + 40/8 = 10+5 = 15 hrs

velocity of the stream = 4 kmph

Speed of the ship in still water is 14 kmph

Speed downstream = (14+4) = 18 kmph

Speed upstream = (14-4) = 10 kmph

Let the distance between Kolkata and Kanyakumari be x km.

Time taken to travel downstream from Kolkata to Kanyakumari + Time taken to travel upstream from Kanyakumari to Chennai (midway) = 38 hours

\Rightarrow \frac{x}{18}+\frac{x/2}{10}=38\ \ \Rightarrow \frac{x}{18}+\frac{x}{20}=38

\Rightarrow \frac{19x}{180}=38\ \ \Rightarrow \frac{x}{180}=2

\therefore x=360\ km

Let the rate upstream of the ship= x kmph

& the rate downstream of the ship = y kmph

Distance travelled upstream in 8⅘  hrs = Distance travelled downstream in 4 hrs.

Since distance is same in both the cases and distance = speed × Time

∴ x × 8⅘ = y × 4

⇒ x × 44/5 = y × 4  ⇒ x × 11/5 = y     ....... (1)

Now, we know that-

Speed in still water = \frac{1}{2} (x+y) km/h

Rate of stream = \frac{1}{2} (y-x) km/h

Hence, Speed Titanic = \frac{x+y}{2}

Speed of water = \frac{y-x}{2}

∴ Required ratio =  \left ( \frac{x+y}{2} \right ) : \left ( \frac{y-x}{2} \right )

= (y+x) : (y-x)

= \left ( \frac{11x}{5}+x \right ) : \left ( \frac{11x}{5}-x \right )

= (11x+5x) : (11x-5x) = 8:3