# Distance and Time Quiz Set 001

### Question 1

A train passes two persons walking in the same direction as the train. The time it takes to move past the man running at 6km/h is 18sec, whereas the time it takes to cross the other man running at 8km/h is 19sec. What is the speed of the train?

A

44km/h.

B

45km/h.

C

43km/h.

D

46km/h.

Soln.
Ans: a

Let the speed of the train be v km/h. Length of the train calculated with the data for the first man = \$(v - 6) × 18\$. It should equal the length obtained from the data for the second man. So \$(v - 6) × 18\$ = \$(v - 8) × 19\$. Please note that we have not converted seconds to hours because that factor will ultimately cancel away. Solving for v we get 44km/h.

### Question 2

A school bus covers a certain distance in 7 hours at a speed of 4 km/h. At what speed should it travel to cover the same distance in 2 hours?

A

14 kmph.

B

15 kmph.

C

13 kmph.

D

16 kmph.

Soln.
Ans: a

Let t1, v1 and t2, v2 be the speeds and times for covering the same distance. We have t1 × v1 = t2 × v2. From here we get v2 = \${7 × 4}/2\$ = 14km/h.

### Question 3

A boy goes to his school at an average speed of 6 km/h, and returns back at an average speed of 3 km/h. What is the average speed for the to and fro journey?

A

4 km/h.

B

5 km/h.

C

3 km/h.

D

\$2{1/3}\$ km/h.

Soln.
Ans: a

If u and v are the to and fro speeds, then the standard formula is \${2uv}/{u + v}\$ = \${2 × 6 × 3}/{6 + 3}\$ = 4 km/h.

### Question 4

Speeds of A and B are in the ratio 7 : 19. What is the ratio of the times that they will take to cover a distance of 100 km?

A

19 : 7.

B

7 : 19.

C

19 : 100.

D

100 : 7.

Soln.
Ans: a

Let the speeds be 7x and 19x. The times they take to cover 100 km are \$100/{7x}\$ and \$100/{19x}\$. The ratio would be 19 : 7.

### Question 5

A car is moving at a speed of 40 meters per second. What is the speed in Km/h?

A

144 kmph.

B

145 kmph.

C

143 kmph.

D

146 kmph.

Soln.
Ans: a

We know 1m/s = \$18/5\$ kmph. So 40m/s = \$18/5 × 40\$ = 144 kmph.