Speed Time And Distance - Study Mode

[#361] A train 300 metres long takes 40 seconds to cross a platform 900 metres long. The speed of the train in, km per hour is :
Correct Answer

(D) 108 km/hr

Explanation

Solution: $$eqalign{
& { ext{Speed of train :}} cr
& = frac{{900 + 300}}{{40}} cr
& = 30{ ext{ m/s}} cr
& { ext{Speed (in km/hr):}} cr
& = 30 imes frac{{18}}{5} cr
& = 108{ ext{ km/hr}} cr} $$

[#362] Rubi goes to a multiplex at the speed of 3 km/hr to see a movie and reaches 5 minutes late. If she travels at the speed of 4 km/hr she reaches 5 minutes early. The the distance of the multiplex from her starting point is :
Correct Answer

(A) 2 km

Explanation

Solution: Time difference = (4 - 3) = 1 hr But, according to the question, 60 × $$frac{1}{6}$$ = 10 minutes So, distance = 12 × $$frac{1}{6}$$ = 2 km

[#363] A train travelling at a speed of 30 m/sec crosses a platform, 600 metres long in 30 seconds. The length (in metres) of train is :
Correct Answer

(D) 300 metres

Explanation

Solution: Total distance covered by the train in 30 seconds with the speed of 30 m/s is = 30 × 30 m/s = 900 metres Total distance - train's length + platform's length 900 = train's length + 600 (when train crosses platform it covers length equal to length of train + length of platform) Train's length = 900 - 600 Train's length = 300 metres

[#364] The distance between place A and B is 999 km. An express train leaves place A at 6 am and runs at a speed of 55.5 km/hr. The train stops on the way for 1 hour 20 minutes. It reaches B at :
Correct Answer

(A) 1.20 am

Explanation

Solution: Time will be taken by train if it does not stop : $$eqalign{
& = frac{{{ ext{Distance }}}}{{{ ext{Speed}}}} cr
& = frac{{999{ ext{ kms}}}}{{55.5{ ext{ km/hr}}}} cr} $$ Without stop = 18 hr But if stops on the way for 1 hour 20 minutes before reaching B. Total time : = 18 hr + 1 hr 20 min = 19 hour 20 minutes Reaching time at B : = 6 am + 19 hr 20 min = 1.20 am

[#365] A man travels some distance at a speed of 12 km/hr and returns at a speed of 9 km/hr. If the total time taken by him is 2 hr 20 min, the distance is :
Correct Answer

(D) 12 km

Explanation

Solution: Let the distance be x km According to the question, $$eqalign{
& frac{x}{{12}} + frac{x}{9} = 2 + frac{{20}}{{60}} cr
& frac{{3x + 4x}}{{36}} = frac{7}{3} cr
& frac{{7x}}{{36}} = frac{7}{3} cr
& x08oxed{x = 12{ ext{ km}}} cr} $$