Arun drove from home to his hostel at 60 miles per hour. While returning home he drove half way along the same route at a speed of 25 miles per hour and then took a bypass road which increased his driving distance by 5 miles, but allowed him to drive at 50 miles per hour along this bypass road. If h

Question

Arun drove from home to his hostel at 60 miles per hour. While returning home he drove half way along the same route at a speed of 25 miles per hour and then took a bypass road which increased his driving distance by 5 miles, but allowed him to drive at 50 miles per hour along this bypass road. If his return journey took 30 minutes more than his onward journey, then the total distance traveled by him is

Accepted Answer

65 miles — Easy Let the one-way distance be $d$. Write the onward time and the (longer) return time, set return $=$ onward $+	frac12$ hour, solve for $d$, then add up every leg actually driven. 1 Onward time. The full distance $d$ at $60$ mph. $$\begin{aligned} &t_{	ext{onward}}=\frac{d}{60} \end{aligned}$$ 2 Return time. First half $	frac{d}{2}$ at $25$ mph, then the bypass of length $	frac{d}{2}+5$ at $50$ mph. $$\begin{aligned} &t_{	ext{return}}=\frac{d/2}{25}+\frac{d/2+5}{50}\ &\Rightarrow\ t_{

CAT 2017 Slot 2 — QA Question 4

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