Question

A car travels 360 km in 4 hrs. Find the distance it covers in 6 hours and 30 minutes at the same speed.

Answer 1

Hint: The distance covered by the car in 4 hrs is 360 km. Now, calculate the speed using the formula, \[\text{Speed=}\dfrac{\text{Distance}}{\text{Time}}\] . Now, convert the time 6 hours and 30 minutes in hours using the relation, \[\text{1hour=60minutes}\] . Then, calculate the distance covered by the car using the formula, \[\text{Distance=Speed }\!\!\times\!\!\text{ Time}\] . Now, solve it further.

Complete step by step answer:
According to the question, it is given that a car travels 360 km in 4 hrs. We have to find the distance covered by the car in 6 hours and 30 minutes at the same speed.
The distance covered by the car = 360 km ……………………………….(1)
The time taken by the car to cover 360 km = 4 hours ……………………………….(2)
We need the speed of the car.
We know the formula, \[\text{Speed=}\dfrac{\text{Distance}}{\text{Time}}\] ………………………………..(3)
In the formula shown in equation (6), we can see that for calculating the speed, we need distance and time.
From equation (1), we have the distance covered by the car and from equation (2) we have the time taken by the car to cover 360 km.
Now, from equation (1), equation (2), and equation (3), we get
\[\text{Speed=}\dfrac{360km}{4hr}=90km/hr\]
So, the speed of the car is 90 km/hr ………………………………..(4)
We need the distance covered by the car in 6 hr and 30 minutes.
The time taken by the car = 6 hour 30 minutes ………………………………..(5)
We know the relation between hour and minutes, \[\text{1hour=60minutes}\] ……………………………(6)
Now, from equation (5) and equation (6), we get
The time taken by the car = 6 hours 30 minutes = \[6\,hours+\dfrac{30}{60}\,hour\] = 6 hours + 0.5 hour = 6.5 hours ………………………………………..(7)
We know the formula, \[\text{Distance=Speed }\!\!\times\!\!\text{ Time}\] ………………………………(8)
In the formula shown in equation (8), we can see that for calculating the distance, we need speed and time.
From equation (4), we have the speed of the car and from equation (5) we have the time taken by the car.
Now, from equation (4), equation (5), and equation (7), we get
\[\text{Distance=90}\,\text{km/hr }\!\!\times\!\!\text{ 6}\text{.5}\,\text{hr=585}\,\text{km}\]
Hence, the distance covered by the car in 6 hours and 30 minutes is 585 km.

Note: We can also solve this question by another method.
The distance covered by the car = 360 km ……………………………….(1)
The time taken by the car to cover 360 km = 4 hours ……………………………….(2)
We know the relation between hour and minutes, \[\text{1hour=60minutes}\] ……………………………………(3)
Now, from equation (2), and equation (3), we get
The time taken by the car to travel = 4 hours = \[4\times 60\,\text{minutes=240}\,\text{minutes}\] …………………………….(4)
The distance covered by the car in 240 minutes = 360 km.
Using the unitary method,
The distance covered by the car in 1 minute = \[\dfrac{360}{240}\] km …………………………………(5)
We have to find the distance covered by the car in 6 hours and 30 minutes.
The time taken by the car = 6 hours and 30 minutes ………………………..(6)
Now, from equation (3) and equation (6), we get
The time taken by car = 6 hours and 30 minutes = \[\text{6 }\!\!\times\!\!\text{ 60minutes+30minutes}\] = 390 minutes ………………………………………(7)
From equation (5), we have
The distance covered by the car in 1 minute = \[\dfrac{360}{240}\] km
Using the unitary method,
The distance covered by the car in 390 minutes = \[\dfrac{360}{240}\times 390\] km = \[\dfrac{3}{2}\times 390\] km = \[3\times 195\] km = 585 km.
Hence, the distance covered by the car in 6 hours and 30 minutes is 585 km.