Time and Distance – Questions and detailed solutions

Question 1. A person covers a distance of 800 meters in 4 minutes. What is their speed in meters per second?

• (a) 3.88 meters per second
• (b) 3.333 meters per second
• (c) 4.01 meters per second
• (d) 5.44 meters per second

Answer

(b) 3.333 meters per second
To calculate the speed in meters per second, we need to convert the time from minutes to seconds.
1 minute is equal to 60 seconds.
So, 4 minutes is equal to 4 x 60 = 240 seconds.
Now, we can calculate the speed:
Speed = Distance / Time
Speed = 800 meters / 240 seconds
Speed ≈ 3.333 meters per second

Question 2. A cyclist covers a distance of 120 km in 6 hours. If the speed is increased by 50%, how long will it take to cover the same distance?

• (a) 3 hours
• (b)2 hours
• (c) 4 hours
• (d) 6 hours

Answer

(c) 4 hours
To calculate the new time it will take to cover the same distance with a 50% increase in speed, we need to find the new speed first.
The initial speed is given by: Speed = Distance / Time
where Distance is 120 km and Time is 6 hours.
Initial Speed = 120 km / 6 hours = 20 km/h
To find the new speed after a 50% increase, we multiply the initial speed by 1.5 (which represents the 50% increase):
New Speed = Initial Speed * 1.5 = 20 km/h * 1.5 = 30 km/h
Now, we can calculate the new time using the new speed and the same distance:
New Time = Distance / New Speed = 120 km / 30 km/h
New Time = 4 hours
Therefore, it will take the cyclist 4 hours to cover the same distance with the increased speed of 50%.

Question 3. A train can travel a distance of 400 km in 4 hours. If the train stops for 20 minutes at a station, what is its average speed in km per hour?

• (a)90.43 km/h
• (b)96.5 km/h
• (c) 82.98 km/h
• (d) 92.3 km/h

Answer

(d) 92.3 km/h
To calculate the average speed of the train, we need to consider the total time it takes to cover the distance, including the time spent at the station.
The train travels a distance of 400 km in 4 hours. However, it stops at a station for 20 minutes, which needs to be accounted for in the total time.
Total Time = Travel Time + Stop Time
Travel Time = 4 hours
Stop Time = 20 minutes = 20/60 hours = 1/3 hours (since 1 hour is equal to 60 minutes)
Total Time = 4 hours + 1/3 hours = 13/3 hours
Now, we can calculate the average speed:
Average Speed = Total Distance / Total Time
Average Speed = 400 km / (13/3) hours
Average Speed = 400 km * (3/13) hours
Average Speed ≈ 92.3 km/h (rounded to one decimal place)
Therefore, the average speed of the train, including the time spent at the station, is approximately 92.3 km/h.

Question 4. A car travels at a speed of 60 kmph for the first 3 hours and then increases its speed by 20%. How far will it travel in the next 2 hours?

• (a)144 km
• (b)120 km
• (c) 122 km
• (d)132 km

Answer

(a) 144 km
To calculate the distance the car will travel in the next 2 hours, we first need to find the speed of the car after the increase.
The initial speed of the car is 60 km/h.
The speed increases by 20%, which means it becomes:
New Speed = Initial Speed + (Initial Speed * 20%) = 60 km/h + (60 km/h * 20%) = 60 km/h + 12 km/h = 72 km/h
Now, we can calculate the distance traveled in the next 2 hours using the new speed:
Distance = Speed * Time
Distance = 72 km/h * 2 hours
Distance = 144 km
Therefore, the car will travel a distance of 144 km in the next 2 hours.

Question 5. A bus covers a distance of 240 km at a speed of 60 kmph. If it wants to reduce the travel time by 1 hour, what should be the increased speed?

• (a)100 km/h
• (b)60 km/h
• (c)40 km/h
• (d) 80 km/h

Answer

(d) 80 km/h
To reduce the travel time by 1 hour, the bus needs to increase its speed. Let’s calculate the original travel time first.
Travel Time = Distance / Speed
Travel Time = 240 km / 60 km/h = 4 hours
Now, we want to reduce the travel time by 1 hour. So the new target travel time is 4 hours – 1 hour = 3 hours.
To find the increased speed needed to achieve the new travel time, we can rearrange the formula:
Speed = Distance / Travel Time
Speed = 240 km / 3 hours
Speed = 80 km/h
Therefore, the bus needs to increase its speed to 80 km/h in order to reduce the travel time by 1 hour.