Question

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

• A. $<26$ Km/h
• B. $>20$ Km/h
• C. $>22$ Km/h
• D. $>26$ Km/h

Answer 1

The correct option is D $>26$ Km/h

Let average running speed $=x$ Km/h
So, average cyling speed $=2x$ Km/h

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

Case 2: Running
Distance $=20$ Km
Average speed $=x$ Km/h
So, time $=\frac{20}{x}...\left(1\right)$
As, Joe complete the race in less than $2.5$ hrs
So, from $\left(1\right)$ and $\left(2\right)$
$\frac{25}{2x}+\frac{20}{x}<2.5$
$\Rightarrow 25+40<5x$
$\Rightarrow x>13$
So, his average speed cycling is greater than $26$ Km/h