Question

Raghubir after travelling 84km , found that if he travelled 5km an hour more ,he would take 5 hrs less, he actually travelled at a rate of:

Answer 1

Distance Raghubir travelled = 84 km
Let his original speed be s km/hr and original time be t hrs

s t = 84....(1)
Now, his speed is = s + 5

and time = t - 5
So, 
(s + 5) (t - 5) = 84
st - 5s + 5t - 25 = 84....(2)
From, (1) we have,
t = 84/s
Putting this in (2), we get
s(84/s) - 5s + 5(84/s) - 25 = 84
84 - 5s + 420/s - 25 = 84
420/s - 5s -25 = 0
420 - 5s² - 25s = 0
s² + 5s - 84 = 0
s² + 12s - 7s - 84 = 0
s(s + 12) - 7(s + 12) = 0
(s + 12)(s - 7) = 0
s = 7 or -12
But speed cant be negative, so s = 7
Therefore, speed of Raghubir is 7 km/hr.