Speed Time And Distance - Study Mode

[#186] A man travels 210 km with the speed of 60 km/hr and next 198 km with the speed of 66 km/hr. Find the average speed of the whole journey.
Correct Answer

(D) 62.8 km/hr
(H) 62.8 km/hr

Explanation

Solution: $$eqalign{
& { ext{Average speed}} = frac{{{ ext{Total distance}}}}{{{ ext{Total time}}}} cr
& = frac{{210 + 198}}{{frac{{210}}{{60}} + frac{{198}}{{66}}}} cr
& = 62.769 cr
& = 62.8,{ ext{km/hr}} cr} $$

[#187] A metro train runs at the speed of 40 km/h from station A to station B covering a distance of 30 km. It stops at 5 stations in between, for 5 minutes at each station. What is the average speed (in km/h) of the train from A to B?
Correct Answer

(B) 25.7

Explanation

Solution: Speed = 40 km/hr Distance = 30 km Time = $$frac{{30}}{{40}}$$ × 60 = 45 min Stoppage time = 5 × 5 = 25 min Total time = 70 min $$eqalign{
& { ext{Average speed}} = frac{{{ ext{Total distance}}}}{{{ ext{Total time}}}} cr
& = frac{{30}}{{70}} imes 60 cr
& = frac{{180}}{7} cr
& = 25.7 cr} $$

[#188] A thief is noticed by a policeman from a distance of 97 m. The thief starts running and the policeman chases him. The thief and the policeman run at a speed of 21 m/sec and 23 m/sec respectively. What is the time taken by the policeman to catch the thief?
Correct Answer

(D) 48.5 sec

Explanation

Solution: Relative speed = 23 - 21 = 2 m/s Time taken by the policeman = $$frac{{97}}{2}$$ = 48.5 sec to catch the thief.

[#189] A person walks a distance from point A to B at 15 km/h, and from point B to A at 30 km/h. If he takes 3 hours to complete the journey, then what is the distance from point A to B?
Correct Answer

(D) 30 km

Explanation

Solution: Distance same Speed = 15 : 3 The distance between A and B = 15 × 2 = 30 km

[#190] The wheel of a car has 210 cm diameter. How many revolutions per minute must the wheel make so that the speed of the car is kept at 120 km/h?
Correct Answer

(C) 303.03

Explanation

Solution: $$eqalign{
& { ext{Diameter}} = 210{ ext{ cm}} cr
& { ext{Radius}} = 105{ ext{ cm}} cr
& { ext{Circumference}} = 2pi r cr
& = 2 imes frac{{22}}{7} imes 105 cr
& = 44 imes 15 cr
& = 660{ ext{ cm}} cr
& { ext{1 hr}} o { ext{120 km}} = 120000{ ext{ m}} cr
& { ext{1 min}} o frac{{120000}}{{60}} = 2000{ ext{ m}} cr
& { ext{Number of revolution}} = frac{{2000 imes 100}}{{660}} = 303.03 cr} $$