Question

If a cyclist had gone 3km. Per hour faster he would have taken 1 hour and 20 minutes less to ride 80 km .what time did he take?

Answer 1

let the speed be x km per hr
$\frac{80}{x} - \frac{80}{x + 3} = \frac{80}{60} = \frac{4}{3} \\ 80( \frac{1}{x} - \frac{1}{x + 3} ) = \frac{4}{3} \\ \frac{x + 3 - x}{ {x}^{2} + 3x } = \frac{4}{3 \times 80} \\ \frac{3}{ {x }^{2} + 3x } = \frac{1}{60} \\ {x}^{2} + 3x = 180 \\ (x + 15)(x - 12) \\ x = - 15 \: (rejected) \\ x = 12$
$speed = \frac{distance}{time} \\ time = \frac{distance}{speed} \\ = \frac{80}{12} \\ = 6 \frac{2}{3} \\ 6 \frac{40}{60} \\ = 6hrs \: and \: 40 \: min$