Question

a man covers a certain distance on scooter. had he moved 3 kmph faster, he would have taken 40 minutes less. if he had moved 2 kmph slower, he would have taken 40 minutes more. the distance is​

Answer 1

Question :

a man covers a certain distance on scooter. had he moved 3 kmph faster, he would have taken 40 minutes less. if he had moved 2 kmph slower, he would have taken 40 minutes more. the distance is

Answer :

12.5 Km

Answer 2

$\red{\textbf{Answer :- 40 km/h}}$

Step-by-step explanation:

$let \: the \: distance \: = x \: km$

$usual \: rate \: = y \: km/h$

$then \:$

⇒$\Large\frac{x}{y} - \frac{x}{y + 3} = \frac{40}{60}$

⇒$\Large \frac{x(y + 3) - xy}{y(y + 3)} = \frac{2}{3}$

⇒$\Large \frac{3x}{y(y + 3)} = \frac{2}{3}$

⇒$2y(y - 2) = 9x$ ________(i)

$and \:\Large \frac{x}{y - 2} - \frac{x}{y} = \frac{40}{60}$

$\Large\frac{xy - x(y - 2)}{y(y - 2)} = \frac{2}{3}$

$\Large\frac{2x}{y(y - 2)} = \frac{2}{3}$

⇒$y(y - 2) = 3x$ ____________(ii)

$on \: dividing \: equation(i) \: by(ii) \: we \: get$

$\Large\frac{2(y + 3)}{y - 2} = 3$

⇒$2y + 6 = 3y - 6$

⇒$y = 12$

$putting \: the \: value \: of \: y \: in \: (i) \: we \: get,$

$2 \times 12 \times 15=9x$

⇒$x = 40 \: km/h$