Answers with Explanations for Time & Distance Practice Problems

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Friends, here are the answers with explanations for our Time and Distance Practice Problems. Please check the practice problems from here and try to solve on your own before checking these solutions. Happy Reading.

1. Average Speed = 2XY / (X+Y)

=> (2 x 80 x 120) / (80 + 120)

= 96 kmph

 2. Distance = 435 m,

Speed = 58 kmph = 58 x (5/18) mps

Time = Distance / Speed

=> 435 / ((58 x (5/18)) = (435 x 18) / (58 x 5) = 27 sec

3. Let the length of the second train be "X" metres.

Distance = 145 + X

Time = 27 sec

Speed = 69-35 = 34 kmph (Same direction)

=> 34 x (5/18) mps

145 + X = 34 x (5/18) x 27

=> X = 255 - 145 = 110

4. Let the actual speed be "S" kmph and time be "t" hours

So,

S.t = (5/8) . S . ((t+(12/60))

=> S = (1/3) x 60 = 20 minutes

5. Average speed = Total Distance / Total Time

=> (220+300) / ((8 hours + (300 km / 60 kmph)) = 520 km / (8+5 hours)

= 520 km / 13 hours = 40 kmph

6. Speed = 91 km / 7 hours = 13 kmph

Boat Speed - Current Speed (Upstream) = 13 kmph

= Boat Speed - 4 = 13

=> Boat Speed = 13+4 = 17 kmph

7. Let the speed of the stream be "X" kmph

Time to travel against stream = 12 / (8-X) hours

Time to travel along with the stream

= 20 / (8+X) hours

So, 12/(8-X) = 20 / (8+X)

=> 12 (8+X) = 20 (8-X)

=> X = 2 kmph

8. Let the distance between A and B be "X" km

So, (X/(12+2) + (X/(12+2)) = 12  => X = 70

9. Let the length of the bridge be "X" km

So, (290 + X) m = 90 x (5/18) mps x 27 sec

=> 290 + X = 675 m  => X=385 m

10. Let the original speed be "S" kmph and original time be "T" hours

Distance = S.T

So, S.T = (S-1) x (9/8) T

=> S = 9 kmph

11. Time taken to complete one round is 42/7 = 6 min

if the diameter increases 5 times, the circumference also increases 5 times

So, New time taken to complete one round is 5 x 6 = 30 minutes

12. Let the speed of the boat be "B" kmph and speed of the current be "C" kmph

So, 4 (B-C) = 44 => B+C = 11

4 (B-C) = 28 => B - C = 7

Solving both the equations, B = 9 kmph

13. Let the distance between his house and office be "X" km

So, (X km / 60 kmph) - (X km / 80 kmph) = ((5-(-3)) / 60 hours

=> X = 32 km

Shortcut Technique :

Required Distance = (Products of Speeds / Difference of Speeds) x Difference in Time

=> ((80 x 60) x (80+60)) x (8/60) = 32 km

14.  Here original time is not required

Required speed = (240 km / 4 hours) = 60 kmph

15. Let the original speed is "X" kmph

So, (180/X) - ((180 / (X+10)) = 54 / 60

=> X = 40 kmph

16. Let the distance between the places be "X" km

=> ((X / (7+3)) + ((X / (7-3)) = 21  => X = 60 km

17. When time is same in each case, the average speed will be the simple average of the speeds

=> Average Speed =  ((45 + 75 + 30) / 3) =  150 / 3

= 50 kmph

18. Let the length of the train be "X" metres

=> ((80 + X) / 100) = ((400+X)/60)

=> X = 200 m

19. Time for meeting each other is 8 hours

The relative speed is 65 + 80 = 145kmph (opposite direction)

So, Distance between A and B

= 145 x 8 = 1160 km

20. Let the speed of the boat be "B" kmph

=> ((60 / (B+)) = ((36 / (B-3))

=> B = 12 kmph 

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