Question

Imran travels a total distance of 180 km. He travels the first 100 km of his journey with an average speed of x km/hr. He travels the rest of his journey at an average speed of 5 km/hr less than the previous speed.
a) Form an expression in terms of x for the time taken for the first 100km of his journey.
b) If the total time taken for the journey is 2 hours and 30 minutes, form an expression and equation and show that it reduces to x² - 77x + 200.

Answer 1

1 Answers


Looks like the the first speed mentioned is for 100 km and not 1 km.

Now, for the first 100 km the speed was 50 km/h.

Therefore, the time taken = 100/50

= 2 hours.

Now for the next 100 km, let us consider the velocity to be v.

So the time taken for covering the next 100 km distance is 100/v

Now, Average speed = Total distance travelled/total time taken foe the journey

So in the above case it is, [(100+100)/(2+{100/v})]

Average speed mentioned is 70 km/kr.

Thus, 70 = [(100+100)/(2+{100/v})]

70 = 200/(2+100/v)



So, 2 + 100/v = 200/70

2 + 100/v = 20/7

100/v = (20/7) -2

100/v = 0.857

v = 100/0.857

v = 116.69 km/hr.