# Time and Distance Questions Answers

• #### 1. How many minutes does Aditya take to cover a distance of 400 m, if he runs at a speed of 20 km/hr

1. \begin{aligned} 1\frac{1}{5} min\end{aligned}
2. \begin{aligned} 2\frac{1}{5} min\end{aligned}
3. \begin{aligned} 3\frac{1}{5} min\end{aligned}
4. \begin{aligned} 4\frac{1}{5} min\end{aligned}

Explanation:

We know that,
\begin{aligned}
Time = \frac{Distance}{Speed} \\
Speed = 20\text{ km/hr} = 20*\frac{5}{18}{ m/sec} \\
= \frac{50}{9}{ m/sec} \\

\text{ Time =} \left(400*\frac{9}{50}\right) \\
= 72 {sec} = 1\frac{1}{5}{ min}
\end{aligned}

• #### 2. A cyclist covers a distance of 750 meter in 2 minutes 30 seconds. What is the speed in km/hr of cyclist

1. 16 km/hr
2. 17 km/hr
3. 18 km/hr
4. 19 km/hr

Explanation:

\begin{aligned}
Speed = \frac{Distance}{Time} \\
Distance = 750 meter \\
Time = \text{2 min 30 sec} = 150 sec \\
Speed = \frac{750}{150} = 5 m/sec \\

=> 5*\frac{18}{5} km/hr = 18 km/hr
\end{aligned}

• #### 3. A car moves at 80 km/hr. What is the speed of the car in meters per second ?

1. \begin{aligned} 20\frac{2}{9} m\sec \end{aligned}
2. \begin{aligned} 22\frac{2}{9} m\sec \end{aligned}
3. \begin{aligned} 24\frac{2}{9} m\sec \end{aligned}
4. \begin{aligned} 26\frac{2}{9} m\sec \end{aligned}

Explanation:

\begin{aligned}
Speed = \left(80*\frac{5}{18}\right) m/sec \\
= \frac{200}{9} m/sec \\
= 22\frac{2}{9} m\sec
\end{aligned}

• #### 4. An athlete runs 200 meters in 24 seconds. His speed is ?

1. 10 km/hr
2. 17 k/hr
3. 27 km/hr
4. 30 km/hr

Explanation:

\begin{aligned}
Speed = \frac{Distance}{Time} \\
= \frac{200}{24}m/sec = \frac{25}{3} m/sec \\
\frac{25}{3}*\frac{18}{5} km/hr = 30 km/hr
\end{aligned}

• #### 5. A person crosses a 600 meter long street in 5 minutes. What is the speed in Km/hr

1. 6.2 km/hr
2. 7.2 km/hr
3. 8.2 km/hr
4. 9.2 km/hr

Explanation:

Two things to give attention on this question.
First time is in minutes, we need to change it to seconds to get speed in m/sec, then we need to get the final answer in km/hr.
So lets solve this.

\begin{aligned}
Speed = \frac{Distance}{Time} \\
Distance = 650 meter \\
Time = \text{5 minutes} = 300 sec \\
Speed = \frac{600}{300} = 2 m/sec \\

=> 2*\frac{18}{5} km/hr = 7.2 km/hr
\end{aligned}

• #### 6. A man is walking at the rate of 5 km/hr crosses a bridge in 15 minutes. The length of the bridge is

1. 1000 meters
2. 1050 meters
3. 1200 meters
4. 1250 meters

Explanation:

We need to get the answer in meters. So we will first of change distance from km/hour to meter/sec by multiplying it with 5/18 and also change 15 minutes to seconds by multiplying it with 60.

\begin{aligned}
Speed = 5* \frac{5}{18} = \frac{25}{18}m/sec \\
Time = 15*60 seconds = 900 seconds \\

Distance = Time * Speed \\
Distance = \frac{25}{18}*900 = 1250 meter
\end{aligned}

• #### 7. A train covers a distance in 50 minutes, if it runs at a speed of 48kmph on an average. Find the speed at which the train must run to reduce the time of journey to 40 minutes.

1. 50 km/hr
2. 60 km/hr
3. 65 km/hr
4. 70 km/hr

Explanation:

We are having time and speed given, so first we will calculate the distance. Then we can get new speed for given time and distance.
Lets solve it.

Time = 50/60 hr = 5/6 hr
Speed = 48 mph
Distance = S*T = 48 * 5/6 = 40 km

New time will be 40 minutes so,
Time = 40/60 hr = 2/3 hr
Now we know,
Speed = Distance/Time
New speed = 40*3/2 kmph = 60kmph