Question

$\text{If the runner in red completes 1 lap in}22\pi \text{seconds,}\text{then how fast does the runner in blue have to run}\text{to complete a lap in the same time?}$

• A. 2 m/s
• B. 3 m/s
• C. 4 m/s
• D. 5 m/s

Answer 1

The correct option is D 5 m/s

$Distancecoveredbythebluerunner=D\left(b\right)$
$Speedofthebluerunner=S\left(b\right)$

For both the runners to finish the lap together, they have to cover their respective laps in the same time.

$Time=\frac{Distance}{Speed}$

$⟹22\pi seconds=\frac{D\left(b\right)}{S\left(b\right)}$

Now, the length of the lap run by the blue runner can be calculated as:

$D\left(b\right)=2\pi \left(radius\right)=2\pi \times (50+5)=110\pi m$

Hence, the speed of the blue runner can be calculated as:

$S\left(b\right)=\frac{110\pi }{22\pi }=5m/s$