# Distance and Time Quiz Set 004

### Question 1

A boy walks along the three edges of an equilateral triangle at average speeds of 5 km/h, 9 km/h and 9 km/h. What is the average speed along the whole journey?

A

\$7{2/19}\$ kmph.

B

\$8{5/9}\$ kmph.

C

\$5{11/21}\$ kmph.

D

\$9{1/7}\$ kmph.

Soln.
Ans: a

Let the edge of the triangle be L. Total distance travelled = 3L. Time taken = \$L/5 + L/9 + L/9\$. So overall average speed = \${3L}/{L/5 + L/9 + L/9}\$ which simplifies to \${135/19}\$, which is same as: \$7{2/19}\$ km/h.

### Question 2

Speeds of A and B are in the ratio 3 : 1. What is the ratio of the times that they will take to cover a distance of 100 km?

A

1 : 3.

B

3 : 1.

C

1 : 100.

D

100 : 3.

Soln.
Ans: a

Let the speeds be 3x and 1x. The times they take to cover 100 km are \$100/{3x}\$ and \$100/{1x}\$. The ratio would be 1 : 3.

### Question 3

Two trains start simultaneously. The first train moves from Jammu to Tawi, whereas the second train moves from Tawi to Jammu. After they meet at a point in between, they respectively take 4 hours and 9 hours to reach their destinations. What is the ratio of their speeds?

A

\${3/2}\$.

B

\${5/2}\$.

C

\${7/2}\$.

D

\${9/4}\$.

Soln.
Ans: a

If they take \$t_1 and t_2\$ hours respectively to reach their destinations, then the ratio of their speeds is \$√t_2 : √t_1\$. So we get \$√9 : √4\$, which gives 3 : 2, or \${3/2}\$.

### Question 4

An aircraft was on a 1360 km journey. Its engine developed a snag so it had to slow down. It's average speed reduced by 5km/h, as a result of which it reached its destination late by 1 hour. What was the actual duration of the journey?

A

16 hrs.

B

17 hrs.

C

15 hrs.

D

18 hrs.

Soln.
Ans: a

Let x be the actual duration of the journey. Then, \$1360/x - 1360/{x + 1} = 5\$. Which gives 1360 × \$1/{x (x + 1)} = 5\$. Solving for x, or by trying the options one by one, we get x = 16 hours.

### Question 5

Speeds of A and B are in the ratio 5 : 8. What is the speed of A if B can cover a distance of 32 Km in 1 hour?

A

20 kmph.

B

21 kmph.

C

19 kmph.

D

22 kmph.

Soln.
Ans: a

The speed of B is 32/1 = 32 km/h. So, the speed of A = \${5 × 32}/8\$ = 20 km/h.