(6) A goods train leaves a station at a certain time at a fixed speed. After 10 hours, an express train leaves the same station and moves in the same direction at a uniform speed of  120 kmph. This train catches the goods train in 5 hours.  Find the speed of  the goods train.

Soln. Goods trains moves for 15 hours and express train moves for 5 hours.

Let, the speed of  goods train is x.

Here, Distances are equal.

i.e.  D₁  =   D₂

∴ S₁T₁  =   S₂T₂

∴ x × 15  =  120 × 5

∴ x   =   8 × 5

=   40 kmph.

Hence, the speed of goods train = 40 kmph.

(7) Walking  at  of  its usual speed, a train is 20 minutes too late. Find its usual time to cover the journey.

Let, the usual time = x min.

∴20 min. late  =   x + 20  min.

Soln. Here, Distances are equal.

i.e.  D₁  =   D₂

∴S₁T₁  =   S₂T₂

( x + 20 )  =  1 × x

∴ 4 ( x + 20 )  =  5x

∴ 4x + 80  =  5x

∴ x  =  80  min.

∴ Usual  time  =   80  minutes.

(8) A  scooterist travels for 14 hours, the first half of  the journey at 36 kmph and the rest at 48 kmph. Find the total distance traveled by him.

Soln. Let the total distance be  2x  km.

  =  14    ⇔  4x + 3x  =  144 × 14  ⇔  2x  =  576  km.

(9) Rakesh can cover a certain distance in 2 hr. 48 min. by covering two-third of  the distance at  4 kmph and the rest at 5 kmph. Find the total  distance.

Soln. 2 hr. 48 min.  =    hrs.  =    hrs.

Let the total distance be 3x km. Then,

  =  ⇔      ⇔     x  =  4   ⇔ 3x  =  12.

∴ Total distance  =  12 km.

(10) An aeroplane travels distance of  2000 km, 1000 km and 500 km at the rate of  500 km/hr, 200 km/hr and  500 km/hr respectively.  Find the average speed.

Soln. Total distance  =  ( 2000 + 1000 + 500 ) km  =  3500 km.

Total time taken  =  hrs  =  10 hrs.

∴ Average Speed  =   km/hr  =  350 km/hr.

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