Q. A car travels a distance of 72 km at a certain average speed of X km per hour and then travels a distance of 81 km at an average speed of 6 km per hour more than its original average speed. If it takes 3 hours to complete the total journey then form a quadratic equation and solve it to find its original average speed.
ICSE Specimen Question Paper (SQP)2025
Ans:
Step 1: Given that the original average speed of the car = X km/ hr
At this speed, time taken to cover 72 km = 
hrs
Next, Average speed of the car in 2nd part of journey = (X + 6) km/hr
∴ at this speed, time taken to cover 81 km = 
hrs
Step 2: Given that total time taken to cover the full journey = 3 hrs
∴ 
∴ 
∴ 72 (X + 6) + 81 X = 3 X (X + 6)
∴ 72 X + 432 + 81 X = 3 X 2 + 18X
∴ 153 X + 432 = 3 X 2 + 18X
∴ 3 X 2 + 18 X – 153 X – 432 = 0
∴ 3 X 2 – 135 X – 432 = 0
∴ X 2 – 45 X – 144 = 0
This is the Quadratic equation for the given question.
Step 3: ∵ X 2 – 45 X – 144 = 0
∴ X 2 – 48 X + 3 X – 144 = 0 (by mid-term splitting)
∴ X (X – 48) + 3 (X – 48) = 0
∴ (X – 48) (X + 3) = 0
∴ X = 48 or X = – 3
Here, we reject X = – 3 because X is the speed and speed can not have negative value
Therefore, the original average speed value is 48 km/hr.
Check:
Time taken in 1st part = 72/X = 72/48 = 3/2 = 1.5 hrs
Time taken in 2nd part = 81/(X + 6) = 81/(48 + 6) = 81/ 54 = 3/2 = 1.5 hrs
Total time taken in journey = 1.5 + 1.5 = 3 hrs
Since it matches with the given condition on the question, hence our solution is correct.
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