Question

The average speed of a car is \[\dfrac{9}{5}\] times the average speed of a bus. A tractor covers 575 km in 23 hours. How much distance will the car cover in 4 hours, if the speed of the bus is twice the speed of the tractor?

Answer 1

Hint: To solve this question we must have the basic knowledge of relation between speed, distance and time.
The relation mentioned above will be used to solve the question.
The relation between speed, distance and time is \[{\text{speed}} = \dfrac{{{\text{distance}}}}{{{\text{time}}}}\]
For solving this question, firstly we will find the speed of the tractor, then we will find the speed of the bus and then the speed of the car. Then we will find the distance travelled by car in 1 hour. At last we will find the distance travelled by the car in 4 hours and this will be our final answer.

Complete step by step answer:
We know that the tractor travels 575 km in 23 hours.
Here,
The distance travelled by the tractor is 575 km.
The time taken by tractor to travel the given distance is 23 hours.
According to the relation between speed, distance and time,
\[
  {\text{speed}} = \dfrac{{{\text{distance}}}}{{{\text{time}}}} \\
  {\text{speed}} = \dfrac{{575{\text{km}}}}{{23{\text{hours}}}} \\
  {\text{speed}} = 25{\text{km}}/{\text{hour}} \\
\]
Hence, the speed of the tractor is \[25{\text{km}}/{\text{hour}}\]
As given in the question, the speed of the bus is twice the speed of the tractor.
Hence the speed of bus is \[50{\text{km}}/{\text{hour}}\]
According to the question,
The average speed of a car is \[\dfrac{9}{5}\] times the speed of a bus.
Hence speed of car is,
\[
  \dfrac{9}{5} \times 50{\text{km}}/{\text{hour}} \\
  90{\text{km}}/{\text{hour}} \\
\]
Now, we need to find the distance travelled by the car in 4 hours.
According to the relation between speed, distance and time,
\[
  {\text{speed}} = \dfrac{{{\text{distance}}}}{{{\text{time}}}} \\
  {\text{distance}} = ({\text{speed}}) \times ({\text{time}}) \\
  {\text{distance}} = (90{\text{km}}/{\text{hour}}) \times (4{\text{hours}}) \\
  {\text{distance}} = 360{\text{km}} \\
 \]

Hence, the distance travelled by the car in the time interval of 4 hours is 360 km.

Note: Sometimes, students forget the relation between speed, distance and time, and apply the wrong relation which leads to the wrong solution. Also, mathematical mistakes happen when we try to solve a question quickly and try to leave some steps, which may also lead to wrong answers. Most students confuse finding the value of the speed of the correct vehicle and finding the speed of another vehicle which may lead to wrong answers.