Test: Speed, Time And Distance- 1

Let time taken to travel the first half = x hr 

Then time taken to travel the second half = (10 - x) hr 

Distance covered in the the first half = 21x [because, distance = time*speed]

Distance covered in the the second half = 24(10 - x)

Distance covered in the the first half = Distance covered in the the second half

So, 21x = 24(10 - x)

=> 45x = 240

=> x = 16/3

Total Distance = 2*21(16/3) = 224 Km [multiplied by 2 as 21x was distance of half way]

According to given condition 

vt=(v+3)(t-2/3)

vt=(v-2)(t+2/3)

here v is velocity in kmph, t is time in hours and 2/3 is value of 40 min in hour on solving we will get t=10/3 and and v = 12 so distance = (10/3) * 12 = 40 kms

If Arun doubles his speed, he needs 3 hour less. Double speed means half time. Hence, half of the time required by Arun to cover 30 km = 3 hour

i.e., Time required by Arun to cover 30 km = 6 hour

Arun's speed 

Due to stoppages, it covers 9 km less.

Time taken to cover 9 km =(9/54 *60)min = 10 min.

Relative speed = Speed of A + Speed of B (∴ they walk in opposite directions) =2+3 = 5 rounds per hour

Therefore, they cross each other 5 times in 1 hour and 2 times in 1/2 hour

Time duration from 8 a.m. to 9.30 a.m. = 1.5 hour

Hence they cross each other 7 times before 9.30 a.m

In this type of questions we need to get the relative speed between them,
The relative speed of the boys = 5.5kmph – 5kmph
= 0.5 kmph

Distance between them is 8.5 km
Time = Distance/Speed
Time= 8.5km / 0.5 kmph = 17 hrs

Given that time taken for riding both ways will be 2 hours lesser than the time needed for waking one way and riding back.

From this, we can understand that time needed for riding one way = time needed for waking one way - 2 hours

Given that time taken in walking one way and riding back = 5 hours 45 min

Hence The time he would take to walk both ways = 5 hours 45 min + 2 hours = 7 hours 45 min

Speed = = 2 m/sec = 2 x (18/5) km/hr = 7.2 km/hr