Question

Malik and Rakesh are best friends who are also neighbours living in Gurugram. Their families are also on exellent terms. 

During summer, they decide to go for a vacation together along with their families to Ahmedabad by their own vehicles.

Malik travels by a Jeep and Rakesh by a car.

Malik's jeep travels at a speed of x km/h and Rakesh's car travels 10 km/h slower than Malik's jeep. Rakesh took 2 hours more than Malik to reach Ahmedabad. The distance between Gurugram and Ahmedabad (by road) is approximately 975 km .

1. What will be the distance covered by Rakesh's car in five hours?
2. Form a quadratic equation to describe the speed of Malik's jeep.
3. What is the speed of Malik's jeep?
4. How much time is taken by Rakesh to reach Ahmedabad?

Answer 1

(i) Given,

The speed of Malik's jeep = x km/h.

Speed of Rakesh's jeep = (x − 10) km/h

Distance covered by Rakesh in 5 hours

= 5(x − 10) km

Hence, distance covered by Rakesh in 5 hours = 5(x − 10) km.

(ii) The distance between Gurugram and Ahmedabad = 975 km

Time taken by Malik = `975/x`

Time taken by Rakesh = `975/(x−10)`

Given, that Rakesh took 2 hours more than Malik to reach Ahmedabad,:

⇒ `975/(x−10) = 975/x + 2`

⇒ `975/(x−10) = (975 + 2x)/x`

⇒ 975x = 975(x − 10) + 2x(x − 10)

⇒ 975x = 975x − 9750 + 2x² − 20x

⇒ 0 = 2x² − 20x − 9750

⇒ 0 = 2(x² − 10x − 4875)

⇒ x² − 10x − 4875 = 0

Hence, quadratic equation is x² − 10x − 4875 = 0.

(iii) From part (ii),

⇒ x² − 75x + 65x − 4875 = 0

⇒ x(x - 75) + 65(x − 75) = 0

⇒ (x − 75)(x + 65) = 0

⇒ (x − 75) = 0 or (x + 65) = 0

⇒ x = 75 or −65

Since speed cannot be negative,

x = 75 km/h

Hence, speed of Malik's jeep = 75 km/h.

(iv) Speed of Rakesh's jeep = x − 10

= 75 − 10

= 65 km/h.

Time taken by Rakesh to reach Ahmedabad =

= `975/65`

= 15 hours.

Hence, Rakesh takes 15 hours to reach Ahmedabad.