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Question

A plane left 30 minutes later than the schedule time and in order to reach its destination 1500 km away in time it has to increase its speed by 250 km/hr from its usual speed. Find its usual speed. [4 MARKS]

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Solution

Framing the equation: 1 Mark
Steps: 2 Marks
Answer: 1 Mark

Let the usual speed of the plane be x km/hr. Then,

Time taken to cover 1500 km with the usual speed =1500xhrs

Time taken to cover 1500 m with the speed of (x+250)km/hr=1500x+250

1500x=1500x+250+12

1500x1500x+250=12

1500x+1500×2501500xx(x+250)=12

1500×250x2+250x=12

750000=x2+250x

x2+250x750000=0

x2+1000x750x750000=0

x(x+1000)(x750)=0

x=1000 or, x=750x=750 [ speed cannot be negative]

Hence, the usual speed of the plane is 750 km/hr.

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