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)
Get the complete, step-by-step math solution for: "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 ...". Powered by SolveForX AI math tutor.
Step-by-Step Solution
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 (TA) and Harish (TH) 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 TA=TH+4. Substituting the expressions for TA and TH, 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 x2+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.