Ashok and Harish are very close friends. They decided to go on a long drive with their families in separate cars. Ashok's car travels at a speed of x km/h, while Harish was driving the car at a speed of 5 km/h faster than Ashok's car. Ashok took 4 hours more than Harish to complete the journey of 400 km. Based on the above information, answer the following questions : (i) Find the distance covered by Harish's car in two hours (in terms of x). (1) (ii) Make a quadratic equation describing the speed of Ashok's car. (1) (iii) (a) Find the speed of Ashok's car (in km/h). (2) OR (b) Find the speed of Harish's car (in km/h). (2)

Step 1: Define speeds and calculate distance for Harish

First, we define the speeds of Ashok's and Harish's cars based on the given information. Ashok's speed is $x$ km/h, and Harish's speed is 5 km/h faster, so it is $(x+5)$ km/h. To find the distance covered by Harish's car in two hours, we multiply his speed by the time.

Step 2: Formulate time taken for each car

The total distance for the journey is 400 km. We use the formula Time = Distance / Speed to express the time taken by Ashok ($T_A$) and Harish ($T_H$) in terms of $x$.

Step 3: Set up the quadratic equation

We are given that Ashok took 4 hours more than Harish. So, we set up the equation $T_A = T_H + 4$. Substituting the expressions for $T_A$ and $T_H$, we then simplify the equation by finding a common denominator and rearranging terms to form a quadratic equation.

Step 4: Solve the quadratic equation for x

We solve the quadratic equation $x^2 + 5x - 500 = 0$ using the quadratic formula. The formula provides two possible values for $x$. Since speed cannot be negative, we discard the negative solution.

Step 5: Calculate speeds

From the quadratic equation, we found $x=20$. This is Ashok's speed. Harish's speed is $x+5$, which is $20+5=25$ km/h.

More from this chapter

• find two natural numbers the sum of 4 squares is 25 times the sum and also equal to 3 times the difference
• Split middle term and factorize X square + 32 x minus 420 is equal 0
• divide 16 into 2 parts such that the twice the square of the largest part exceeds the square of the smaller part by 164
• एक्स स्क्वायर + 24 + 12 सॉल्व करो
• Solve: x² − 5x + 6 = 0 vdhsjv
• Solve: x² − 5x + 6 = l don't know
• 19. The perimeter of a right triangle is 60 cm and its hypotenuse is 25 cm. Find the lengths of other two sides of the triangle.
• The time taken by a person to travel an upward distance of 150 km was 2(1)/(2) hours more than the time taken in the downward return journey. If he returned at

All Quadratic Equations solutions →