Pawan Prajapati
Last Activity: 3 Years ago
Hint: Let the time for traveling at a constant speed from P to Q be xy
where x be the distance and y be the speed. Now if the speed was increased by 10 km/hr then the time will be xy + 10 and since it would have taken 1 hour less then xy−xy + 10=1
. Simplify it and form an equation. Form another equation by following the same process for when speed is increased further by 10 km/hr. Solve the equations to find the value of x.
Complete step-by-step answer:
Given, a car travels from city P to Q at a constant speed. Let the distance be x m and speed be y km/hr. Then the time taken will be=distancespeed=xy
Now if the speed was increased by 10 km/hr, it. So the time taken will be xy + 10.Since it would have taken 1 hour lesser to cover the distance, then
⇒ xy−1=xy + 10 ⇒xy−xy + 10=1
On simplifying the equation we get,
⇒xy + 10x - xyy(y + 10)=1⇒10x = y2+10y
⇒y2 + 10y - 10x = 0 ---- (i)
Now if the speed is further increased by 10 km/hr then the total speed will be y + 20 km/hr. The time will be further decreased by 45 minutes, so the lesser time will be 1hr45min.
1hr45min=1+4560=1+912=2112=74hrs
So then according to question,
⇒xy−xy + 20=74⇒xy + 20x - xyy2 + 20y=74
On simplifying we get,
⇒80x = 7y2 + 140y⇒7y2 + 140y - 80x = 0 --- (ii)
On putting the value of x from eq. (i) into (ii) we get,
⇒7y2 + 140y - 80(y2 + 10y10) = 0
⇒7y2 + 140y - 8y2 - 80y = 0
⇒−y2 + 60y - = 0⇒y2 = 60y
⇒ y = 60
On putting the value of y in eq.(i) we get,
⇒602 + 10×60 - 10x = 0⇒3600 + 600 - 10x = 0
⇒10x = 4200⇒x = 420010=420 Km
Hence the distance between the 2 cities is 420 km.
Note: The question can also be solved by this method-
We know that distance (d) = speed(s) × time (t) and we have to find the distance (d) in the given question. Since when speed (s) is increased by 10 the time (t) is decreased by 1 hour. Now in the second statement it says that when speed is increased by 20 the time is decreased by 45 minutes which can be written as 7/4hours, then we can write the coefficients of s and t as
We can cross multiply the coefficients of s and t to form the equation. So the equations will be −s + 10t = 10 and - 74s + 20t = 35. On solving these eq., we get t = 7hrs and s = 60km/hr.Now put the values in the formula of distance and you’ll get the answer.
