Question

A student riding a bicycle on a $5km$ one way street takes $40min$ to reach home. The student stopped for $15min$. During the ride $60$ vehicles overtook the student (assume the no. of vehicles overtaken by the students is zero) during the ride and $45$ vehicles while the student stopped. The speed of vehicles stream on that road (in km/hr.) is.

• A. $7.5$
• B. $12$
• C. $40$
• D. $60$

Answer 1

The correct option is D $60$

Velocity of student $=\frac{5km}{(40-15)min}$
$=12km/hr$

$[\frac{vehicle/min}{Relativespeedofvehiclew.r.tstudent}{]}_{moving}$

$=[\frac{vehicle/min}{Relativespeedofvehiclew.r.tstudent}{]}_{standing}$

$\Rightarrow \frac{60/25}{x-12}=\frac{45/15}{x-0}$
$\Rightarrow x=60km/hr$

Alternatively,
Traffic flow(q)$=\frac{45veh.}{\left(15/60\right)hr.}=180veh/hr$
$60=qt-kL$
$60=(180\times \frac{25}{60})-(k\times 5)$
$\Rightarrow k=3$
$kv=q=180$
$v=60km/hr$