Question

Joe enters a race where he has to cycle and run, he cycles a distance of $25\text{km}$, and then runs for $20\text{km}$. His average running speed is half of his average cycling speed.
Joe completes the race in less than $2.5\text{hrs}$ hrs, then the average speed of Joe throughout the race is

Answer 1

Let average running speed $=x\text{Km/h}$
So, average cyling speed $=2x\text{Km/h}$

Case 1: Cycling
Distance $=25$ Km
Average speed $=2x$ Km/h
$\text{So, time}=\frac{25}{2x}...\left(1\right)$

Case 2: Running
Distance $=20$ Km
Average speed $=x$ Km/h
$\text{So, time}=\frac{20}{x}...\left(1\right)$
As, Joe complete the race in less than $2.5$ hrs
Total time taken $<2.5$
So, from $\left(1\right)$ and $\left(2\right)$
$\frac{25}{2x}+\frac{20}{x}<2.5$
$\Rightarrow 25+40<5x$
$\Rightarrow x>13$

average cyling speed $=2x\text{Km/h}$

So, his average speed cycling is greater than $26$ Km/h
Hence the correct answer is Option D.