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A car travels from P to Q at a constant speed. If the speed were increased by 10 km/hr, it would have taken 1 hour less to cover the distance. It would have taken further 45 minutes lesser if the speed was further increased by 10 km/hr. What is the distance between the two cities?

A car travels from P to Q at a constant speed. If the speed were increased by 10 km/hr, it would have taken 1 hour less to cover the distance. It would have taken further 45 minutes lesser if the speed was further increased by 10 km/hr. What is the distance between the two cities?

Grade:12th pass

1 Answers

Pawan Prajapati
askIITians Faculty 9723 Points
20 days 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.

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