# Distance and Time Quiz Set 009

### Question 1

A cyclist travels at a speed of 8km/h. Had he travelled at 10km/h he would have covered a distance of 6 km more. What is the total distance travelled by him?

A

24 km.

B

25 km.

C

23 km.

D

26 km.

Soln.
Ans: a

By the given problem, the time is same for both cases. If the total distance covered by him at 8km/h is x, then, \$x/8 = {x + 6}/10\$. Solving, we obtain x = 24 km.

### Question 2

A boy walks along the three edges of an equilateral triangle at average speeds of 6 km/h, 2 km/h and 9 km/h. What is the average speed along the whole journey?

A

\$3{6/7}\$ kmph.

B

\$5{2/3}\$ kmph.

C

\$2{2/9}\$ kmph.

D

\$5{1/3}\$ kmph.

Soln.
Ans: a

Let the edge of the triangle be L. Total distance travelled = 3L. Time taken = \$L/6 + L/2 + L/9\$. So overall average speed = \${3L}/{L/6 + L/2 + L/9}\$ which simplifies to \${27/7}\$, which is same as: \$3{6/7}\$ km/h.

### Question 3

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.

### Question 4

A school bus covers a certain distance in 2 hours at a speed of 48 km/h. At what speed should it travel to cover the same distance in 6 hours?

A

16 kmph.

B

17 kmph.

C

15 kmph.

D

18 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 = \${2 × 48}/6\$ = 16km/h.

### Question 5

A car is moving at a speed of 72 kmph. What is the speed in m/s?

A

20 m/s.

B

21 m/s.

C

19 m/s.

D

22 m/s.

Soln.
Ans: a

We know 1kmph = \$5/18\$ m/s. So 72kmph = \$5/18 × 72\$ = 20 m/s.