# Distance and Time Quiz Set 007

### Question 1

A boy goes to his school at an average speed of 5 km/h, and returns back at an average speed of 6 km/h. What is the average speed for the to and fro journey?

A

\$5{5/11}\$ km/h.

B

\$7{1/10}\$ km/h.

C

\$3{10/13}\$ km/h.

D

\$7{2/13}\$ km/h.

Soln.
Ans: a

If u and v are the to and fro speeds, then the standard formula is \${2uv}/{u + v}\$ = \${2 × 5 × 6}/{5 + 6}\$ = \${60/11}\$, which is same as: \$5{5/11}\$ km/h.

### Question 2

A vehicle travels 50% of its distance at 3 km/h, and the remaining 50% at 7 km/h. What is the total distance, if it travelled for a total duration of 20 hours?

A

84 km.

B

85 km.

C

83 km.

D

86 km.

Soln.
Ans: a

Let 2x be the actual duration of the journey. Then, \$x/3 + x/7 = 20\$. Solving for x we get x = 42, and so, 2x = 84 km.

### Question 3

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 4

Two steamers X and Y travel towards a destination 192 km away. If Y travels 2 times faster than X, then it reaches 16 hours early. What is the speed of X?

A

6 kmph.

B

7 kmph.

C

5 kmph.

D

8 kmph.

Soln.
Ans: a

Let x be the speed of X, then the speed of Y is 2x. So \$192/x - 192/{2 × x} = 16.\$ Solving, we get x = 6 km/h.

### Question 5

Two steamers X and Y travel towards a destination 2772 km away. If Y travels 14 times faster than X, then it reaches 11 hours early. What is the speed of X?

A

234 kmph.

B

235 kmph.

C

233 kmph.

D

236 kmph.

Soln.
Ans: a

Let x be the speed of X, then the speed of Y is 14x. So \$2772/x - 2772/{14 × x} = 11.\$ Solving, we get x = 234 km/h. 