Nidhi and Ria are very close friends. Nidhi’s parents own a Maruti Alto. Ria’s parents own a Toyota Liva. Both the families decide to go for a picnic to Somnath temple in Gujrat by their own cars. Nidhi’s car travels x km/h while Ria’s car travels 5 km/h more than Nidhi’s car. Nidhi’s car took 4 hrs more than Ria’s car in covering 400 km. (i) What will be the distance covered by Ria’s car in two hour? (a) 2 (x+5) km (b) (x – 5) km (c) 2 (x + 10) km (d) (2x+5) km ii) Which of the following quadratic equation describe the speed of Nidhi’s car? (a) x2 − 5x − 500 = 0 (b) x2 + 4x − 400 = 0 (c) x2 + 5x − 500 = 0 (d) x2 − 4x + 400 = 0 (iii) What is the the speed of Nidhi’s car? (a) 20 km/hour (b) 15 km/hour (c) 25 km/hour (d) 10 km/hour (iv) How much time took Ria to travel 400 km? (a) 20 hour (b) 40 hour (c) 25 hour (d) 16 hour (v) What is the speed of Rias car. (a) 20km/hr (b) 25km/hr (c) 30km/hr (d) 15km/hr
Answers
Given : Nidhi’s car travels x km/h while
Ria’s car travels 5 km/h more than Nidhi’s car.
Nidhi’s car took 4 hrs more than Ria’s car in covering 400 km.
To Find : What will be the distance covered by Ria’s car in two hour?
(a) 2(x + 5) km , (b) (x - 5) km , (c) 2(x + 10) km , (d) (2x + 5) km
quadratic equation describe the speed of Nidhi’s car
speed of Nidhi’s car
Solution:
Nidhi’s car speed = x km/h
Ria’s car travels 5 km/h more than Nidhi’s car.
=> Ria’s car speed = x+ 5 km/h
Distance = Speed x Time
distance covered by Ria’s car in two hour = (x + 5) 2
= 2(x + 5) km
(a) 2(x + 5) km
400/x = 400/(x + 5) + 4
=> 100(x + 5) = 100x + x(x + 5)
=> 100x + 500 = 100x + x² + 5x
=> x² + 5x - 500 = 0
quadratic equation describe the speed of Nidhi’s car x² + 5x - 500 = 0
x² + 5x - 500 = 0
=> (x + 25)(x - 20) = 0
=> x = 20
Nidhi’s car speed = 20 km/hr
Ria car speed = 25 km/hr
time taken by Ria to travel 400 km = 400/25 = 16 hrs
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