Question
A runner travels from point ‘E’ to ‘F’ at a
constant speed. If the speed was increased by 12 km/h, it would have taken 2.5 hours less to cover the distance. It would have taken further 1 hour less if the speed was further increased by 12 km/h. The distance between point ‘E’ and point ‘F’ is:Solution
According to the question, Let the original speed of the runner be ‘x’ km/h and the original time taken to reach the destination be ‘t’ hours. So, the distance between point ‘E’ and ‘F’ = x × t = xt km So, xt/(x + 12) = t – 2.5..........................(1) And, xt/(x + 24) = t – 2.5 – 1 Or, xt/(x + 24) = t – 3.5........................(2) Dividing equation (1) by equation (2), we get (x + 24)/(x + 12) = (t – 2.5)/(t – 3.5) So, xt – 48 – 12x + 24t = xt + 12t – x – 48 Or, 12t – 12x = 48 Or, x = t – 4 Putting the value of ‘x’ in equation (1), we get 12t² – 30t = 12t² – 45t + 60 Or, t = 6 So, x = 6 – 4 = 2 Desired distance = 6 × 2 = 12 km
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