Q6 of 83 Page 88

If a cyclist travels at a speed 2 km/hr more than his usual speed, he reaches the destination 2 hours earlier. If the destination is 35 km away, what is the usual speed of the cyclist?

Distance = 35 km


Let the usual speed be x


And t be the time taken to reach destination when speed is x




…(i)


If he travels at a speed (x + 2) km/hour time taken is (t – 2) hours


Distance is same 35 km


Speed =



Using (i)





⇒ (x + 2)(35 – 2x) = 35x


⇒– 2x2 + 70 – 4x = 0


divide by – 2


⇒ x2 + 2x – 35 = 0


⇒ x2 + 7x – 5x – 35 = 0


taking x common from first two terms and – 5 common from next two


⇒ x(x + 7) – 5(x + 7) = 0


⇒ (x – 5)(x + 7) = 0


⇒ (x – 5) = 0 or (x + 7) = 0


Thus x = 5 and not 7 because x represent speed and speed cannot be negative


The usual speed of cyclist = 5 km/hour


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