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) x
2
− 5x − 500 = 0
(b) x
2+ 4x − 400 = 0
(c) x
2+ 5x − 500 = 0
(d) x
2
− 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 hours
(b) 40 hours
(c) 25 hours
(d) 16 hours
(v) If Ria’s car travels in a speed of 120 km/hr in 2 hours then what is the
distance covered?
(a) 60 km
(b) 40 km
(c) 25 km
(d) 30 km
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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Answer:
a.) 2(x+5)
b.) x^2+5x-500
c.)20 km/hr
Step-by-step explanation: