Speed Time And Distance - Study Mode

[#141] A car driver, driving in a fog, passes a pedestrian who was walking at the rate of 2 km/h in the same direction. The pedestrian could see the car for 6 minutes and it was visible to him up to distance of 0.6 km. what was speed of the car?
Correct Answer

(D) 8 kmph

Explanation

Solution: In 6 minutes, the car goes ahead by 0.6 km. Hence, the relative speed of the car with respect to the pedestrian is equal to 6 kmph. Hence, Net speed of the car is 8 kmph.

[#142] A cyclist moving on a circular track of radius 100 meters completes one revolution in 2 minutes. What is the average speed of cyclist (approx.)?
Correct Answer

(A) 314 m/min

Explanation

Solution: Distance covered in one complete revolution $$eqalign{
& = 2pi r cr
& = frac{{2 imes 100 imes 22}}{7} cr
& approx 628,m cr
& { ext{Average}},{ ext{speed}} cr
& = frac{{628}}{2} cr
& = 314,m/min cr} $$

[#143] Between 5 am and 5 pm of a particular day for how many times are the minute and the hour hands together?
Correct Answer

(A) 11

Explanation

Solution: It will come 11 times together.

[#144] Two rifles are fired from the same place at a difference of 11 minutes 45 seconds. But a man who is coming towards the place in a train hears the second sound after 11 minutes. Find the speed of train. (speed of sound = 330 m/s)
Correct Answer

(C) 81 kmph

Explanation

Solution: Distance travelled by man-train in 11 minute = distance traveled by sound in (11 min 45 sec - 11 min) = 45 sec.
Let the speed of train be x kmph. Now, Or, $$x imes frac{{11}}{{60}} = frac{{45}}{{3600}} imes 330 imes frac{{18}}{5}$$ Or, x = 81 kmph.

[#145] A train travels at a speed of 30 km/hr for 12 minutes and at a speed of 45 km/hr for the next 8 minutes. The average speed of the train for this journey is :
Correct Answer

(B) 36 km/hr

Explanation

Solution: Total distance travelled : $$eqalign{
& = left( {30 imes frac{{12}}{{60}} + 45 imes frac{8}{{60{ ext{ }}}}}
ight){ ext{ km}} cr
& = { ext{12 km}} cr} $$ Total time taken : = (12 + 8) min = 20 min = $$frac{1}{3}$$ hr ∴ Average speed : = (12 × 3) km/hr = 36 km/hr