# Time and Distance - Aptitude Questions and Answers Part 2

6. On his way to office, Rohan's taxi driver drives him at a speed of 30 kmph and reaches late by one-third of an hour. Next morning, he drives at a speed of 45 kmph but is still 8 minutes late. Find the distance between his home and office?

a. 18 km
b. 20 km
c. 27 km
d. 35 km

Explanation:

D = S x T
 ∴ S = D ; T = D T S

Let distance be D
With speed 30km/hr he is 20 minutes (one-third of an hour) late
With speed 45 km/hr he is 8 minutes late
 ∴ Difference between two times = 20-8 = 12 min = 12 hours 60

Tip:
Difference between two given times can also be easily measured or checked by looking at a watch or imagining a watch.

 Also, time = T = D S
 ∴ D - D = 12 30 45 60
∴ D = 18 km

7. A child goes to school on bike at a speed of 18 km/h.  While coming back, he take school bus which runs faster by 27 km/h. What is his average speed for the entire journey?

a. 25.71 km/hr
b. 27 km/hr
c. 27.39 km/hr
d. 31.5km/hr

Explanation:

D = S x T
 ∴ S = D ; T = D T S

 Speed = S = D T
 Average Speed = Total distance travelled Total time taken
Let distance between start and end be D
Total distance travelled = D+D = 2D
The bus runs 27 kmph faster, so its speed is 45 kmph.
 Total Time = t1+t2 = d1 + d2 = D + D s1 s2 18 45
 ∴ Average speed = 2D = 25.71 km/hr D/18 + D/45

8. A friend of mine covers a total distance of 325 km from his hotel to village by three different modes.  He travels first 96 km in a rickshaw, 124 km by bus and 105 km by bullock cart. The speed of rickshaw is 16 km/hr, bus is 31 km/h and bullock cart is 7 km/h. What is his average speed for the entire travel?

a. 13 km/hr
b. 14.25 km/hr
c. 18 km/hr
d. 16.75 km/hr

Explanation:

D = S x T
 ∴ S = D ; T = D T S

 Speed = S = D T
 Average Speed = Total distance travelled Total time taken
Total distance = 96 + 124 + 105 = 325 km
 Total Time = t1+t2+t3 = d1 + d2 + d3 = 96 + 124 + 105 = 25 hours s1 s2 s3 16 31 7
 ∴ Average speed = 325 = 13 km/hr 25

9. Rajat travels from City A to City B. He travels first 25% of the distance at 20 kmph, next 25% of the distance at half the earlier speed and the remaining distance at 80 kmph. Find his average speed for the travel.

a. 22.85 km/hr
b. 25.15 km/hr
c. 40 km/hr
d. 50 km/hr

Explanation:

D = S x T
 ∴ S = D ; T = D T S

 Speed = S = D T
 Average Speed = Total distance travelled Total time taken
Let Total distance = D km
 Parts of the distance = D ; D ; remaining distance. 4 4
 Remaining distance = D - ( D + D ) = D 4 4 2
Half the earlier speed in second segment of travel = 10 kmph
 Total Time = t1+t2+t3 = D + D + D = D + D + D = 7D 4 x 20 4 x 10 2 x 80 80 40 160 160
 ∴ Average speed = D = 22.85 km/hr 7D/160

10. To meet a friend in 6 minutes, Reeta drives at 40 kmph. If she could take 2 minutes more to meet her friend, at what speed could she drive?

a. 15 km/hr
b. 18 km/hr
c. 21 km/hr
d. 30 km/hr