Question

A man covers a distance on scooter. Had he moved 3 kmph faster he would have taken 40 min less. If he had moved 2 kmph slower he would have taken 40min more. What is the distance he wanted to cover?

Answer 1

40 km

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Let distance be the x km and y be the usual speed and t be the time,
=> t = x/y......(1).
Since, speed is inversely prop. to time. i.e. faster speed -> slower time.
Now, original time(t)- slow time(t1) => x/y - x/y+3 = 40/60 => 9x = 2y(y+3)........(2).
And, fast time(t2) - original time(t) => x/y-2 - x/y = 40/60 => 6x = 2y(y-2)........(3)
So dividing (2) by (3) we get y=12 km/hr
Now put y= 12 in (2) we get,
9x = 24(12+3) => x = 24*15/9 = 5*8 = 40.
Hence distance = 40 km