ICOME
    FOLLOW US: facebook twitter instagram youtube
JOIN ICOME
JOIN ICOME
JOIN ICOME

Time and Distance

Theory and Formula


Question

Q1. The distance between two cities A and B is 100 km Car travels from A to B aat the rate of 40km/h , and back to A at the rate of 60 km/h . Find the average speed .

Solution.
Average speed =
2xy/x+y


=
2x60x40/60+40
=
4800/100
= 48km/h
Solution

Q2. A person covers a certain distance between his house and office by car . It he moves at the rate of 40km/h , he is late by 10 min, and if he travels at the speed of 60km/his reaches his office 20 min earlier find the distance between house and office .

Let the distance be x km

x/40
-
x/60
=
1/2
  ⇒  
60x - 40x/60 x 40
=
1/2


20x/2400
=
1/2
 ⇒   4x = 240   ⇒   x = 60km/h
Solution

Q3. A man walking with a speed 8km/h reaches his office 15 minutes late . If he walks at a speed of 12km/h he reaches on time . find the distance between his office and house .

Solution.
Let x is distance ,
x/8
-
x/12
=
15/60
  ⇒   
4x/96
=
1/4


16x = 96   ⇒    x = 6 km
Solution

Q4. An athalete runs 200 m in 24 sec . find his speed in km/h

Solution.
200/24
m/s   ⇒   
200/24
x
18/5
= 30km/h
Solution

Q5. The distance between two places P and Q is 42 km . Person A moves at the rate of 3km/h towards P to Q (start as P) and another person moves xkm/h towards Q to P (start at Q). They meet each other after 6 hours . find the value of x .

Solution.
They move in opposite direction so their relative speed is (3+x)

(3+x)6 = 42   ⇒   18 + 6x = 42   ⇒    18 + 6x = 42   ⇒    6x = 24

x = 4km/h
Solution

Q6. Running 5/3 of his usual speed , a person improves his timing by 5 minutes, find his usual time to cover the distance .

(a) 20 minutes (b) 12.5 minutes (c) 10 minutes (d) 16 minutes

Solution.
(b) 12.5 minutes
Solution

Q7. A train travelling 20 km/hr leaves place A at 8 am and another train travelling 30 km/hr starts at 2 p.m in the same direction. How many km from place A will they be together ?

(a) 60 km (b) 300 km (c) 200 km (d) 150 km

Solution.
(b) 300 km
Solution

Q8. Two stations P and Q are 110 km apart on a track. one train starts from P to Q at 9 am at 40km/hr. Another train starts from Q to P at 11 am at 50 km/hr . At what time both train will meet ?

(a) 1 pm (b) 12:10 pm (c) 11:20 am (d) 11 am

Solution.
(c) 11:20 am
Solution

Q9. A man covers a certain distance between two places on scooter, with the speed of 30 km/hr , he take by 20 min. However with the speed of 40 km/hr he reaches his office 10 min earlier . find the distance between two places .

(a) 60 km (b) 30 km (c) 64 km (d) 38 km

Solution.
(a) 60 km
Solution

Q10. Two cars run to a place at the speeds of 45 km/hr and 50 km/hr respectively. If the second cars takes 5 hrs less than the first for journey , find the length of the journey.

(a) 1890 km (b) 2000 km (c) 2400 km (d) 2250 km

Solution.
45 x 50/ 5
x 5

= 2250 km
Solution