# Distance and Time Quiz Set 016

### Question 1

Two cars, A and B, start to move towards each other. If they meet when A has travelled \$(1/6)\$th of the distance, what is the ratio of the speed of B to the speed of A?

A

5.

B

6.

C

4.

D

7.

Soln.
Ans: a

Let the speeds of the cars be u and v and the initial distance between them be L. When they meet they have travelled for the same time. So \$(L/6)/u = ({5L}/6)/v\$. The ratio \$v/u\$ = 5.

### Question 2

Two cars A and B begin to move towards each other and meet midway after travelling equal distance. What is the initial distance between them if the speeds of A and B are 4 km/h and 8 km/h, and B started 1 hour late?

A

16 km.

B

17 km.

C

15 km.

D

\$6{1/3}\$ km.

Soln.
Ans: a

If the distance between them is L, they meet after travelling L/2. Equating the times they travelled, \$L/{2 × 4} = L/{2 × 8} + 1\$. Solving for L we get L = 16 km.

### Question 3

A train takes 3 hours less if its speed is increased by 2 km/hr. What is the normal speed if the distance is 12km?

A

2.

B

3.

C

5.

D

4.

Soln.
Ans: a

Let the normal speed be x km/hr. We have been given \$12/x\$ - \$12/{x + 2}\$ = 3. This translates to the quadratic equation \$3x^2 + 6x - 24 = 0\$, which can be solved to obtain x = 2 as the answer. If you don't want to solve the equation, then you can put each option into this equation and check that way. But this trick will work only if all the options have some numerical value.

### Question 4

Two trains start simultaneously. The first train moves from A to B, whereas the second train moves from B to A. After they meet at a point in between, they respectively take 144 hours and 49 hours to reach their destinations. What is the ratio of their speeds?

A

\${7/12}\$.

B

\${19/11}\$.

C

\${31/14}\$.

D

\${43/14}\$.

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 \$√49 : √144\$, which gives 7 : 12, or \${7/12}\$.

### Question 5

An object covers a distance of 1400 meters in 21 minutes. What is its speed?

A

4 kmph.

B

5 kmph.

C

3 kmph.

D

6 kmph.

Soln.
Ans: a

The speed = distance/time. It is \$1400/{21 × 60}\$ × \$18/5\$ = 4 kmph.